1. a. Find an equation of the sphere that passes through the point and has center .
b. Find the curve in which this sphere intersects the xy-plane.
2. Write an inequality to describe the half-space consisting of all po
...
1. a. Find an equation of the sphere that passes through the point and has center .
b. Find the curve in which this sphere intersects the xy-plane.
2. Write an inequality to describe the half-space consisting of all points to the left of a plane parallel to
the xz-plane and units to the right of it.
3. Write inequalities to describe the solid rectangular box in the first octant bounded by the
planes , , and .
4. Find an equation of the sphere that passes through the point and has center .
5. Draw a rectangular box with the origin and as opposite vertices and with its faces parallel to
the coordinate planes. Find the length of the diagonal of the box.
6. Write inequalities to describe the solid upper hemisphere of the sphere of radius centered at the origin.
7. Find the length of the median of side AB of the triangle with vertices
8. A woman walks due west on the deck of a ship at mi/h. The ship is moving north at a speed of
mi/h. Find the speed of the woman relative to the surface of the water. Round the result to the
nearest tenth.
9. The tension T at each end of the chain has magnitude N and makes an angle with the
horizontal. What is the weight of the chain? Round the result to the nearest hundredth.
10. Velocities have both direction and magnitude and thus are vectors. The magnitude of a velocity
vector is called speed. Suppose that a wind is blowing from the direction N W at a speed of
km/h. (This means that the direction from which the wind blows is west of the northerly
direction.) A pilot is steering a plane in the direction N E at an airspeed (speed in still air) of
km/h. The true course, or track, of the plane is the direction of the resultant of the velocity
vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant.
Find the ground speed of the plane. Round the result to the nearest hundredth.Stewart - Calculus ET 8e Chapter 12 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
11. Calculate the given quantities if
12. A bicycle pedal is pushed by a foot with a force of a-N as shown. The shaft of the pedal is cm
long.
Find the magnitude of the torque about P correct to two decimal places.
Let , , .
13. Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.
14. Find the equation of the line through and perpendicular to the plane
15. Find parametric equations for the line through and
16. Find an equation of the plane that passes through the line of intersection of the planes and
is perpendicular to the plane
17. Find parametric equations for the line through and parallel to the vector
18. Find the point of intersection.Stewart - Calculus ET 8e Chapter 12 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
19. Find an equation of the plane through the origin and parallel to the plane
20. Find an equation for the surface obtained by rotating the line about the x-axis.Stewart - Calculus ET 8e Chapter 12 Form A
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2.
3.
4.
5.
6.
7. 3 38
8.
9.
10.
11.
12.
13. 4
14.
15.
16.
17.
18.
19.
20.Stewart – Calculus ET 8e Chapter 12 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. a. Find an equation of the sphere that passes through the point and has center .
b. Find the curve in which this sphere intersects the xy-plane.
2. Write an inequality to describe the half-space consisting of all points to the left of a plane parallel to
the xz-plane and units to the right of it.
3. Write inequalities to describe the solid rectangular box in the first octant bounded by the
planes , , and .
4. Write an inequality to describe the region consisting of all points between (but not on) the
spheres of radius and centered at the origin.
5. Find an equation of the sphere that passes through the point and has center .
6. Draw a rectangular box with the origin and as opposite vertices and with its faces parallel to
the coordinate planes. Find the length of the diagonal of the box.
7. Write inequalities to describe the solid upper hemisphere of the sphere of radius centered at the origin.
8. Find the length of the median of side AB of the triangle with vertices
9. A woman walks due west on the deck of a ship at mi/h. The ship is moving north at a speed of
mi/h. Find the speed of the woman relative to the surface of the water. Round the result to the
nearest tenth.
10. Calculate the given quantities ifStewart – Calculus ET 8e Chapter 12 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
11. A bicycle pedal is pushed by a foot with a force of a-N as shown. The shaft of the pedal is cm
long.
Find the magnitude of the torque about P correct to two decimal places.
Let , , .
12. Find the magnitude of the torque about P correct to two decimal places if a d-lb force is applied as
shown. Let ft, ft, , lb.
13. Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.
14. Find the equation of the line through and perpendicular to the plane
15. Find parametric equations for the line through and
16. Find an equation of the plane that passes through the line of intersection of the planes and
is perpendicular to the plane
17. Find parametric equations for the line through and parallel to the vectorStewart – Calculus ET 8e Chapter 12 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
18. Find the point of intersection.
19. Find an equation of the plane through the origin and parallel to the plane
20. Find an equation for the surface obtained by rotating the line about the x-axis.Stewart – Calculus ET 8e Chapter 12 Form B
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2.
3.
4.
5.
6.
7.
8. 9 5
9.
10.
11.
12. 101.08 ft-lb
13. 4
14.
15.
16.
17.
18.
19.
20.Stewart - Calculus ET 8e Chapter 12 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Select the correct answer for each question.
____ 1. Suppose you start at the origin, move along the x-axis a distance of units in the positive direction,
and then move downward a distance of units. What are the coordinates of your position?
a.
b.
c.
d.
e.
____ 2. Find the center and radius of the sphere.
a.
b.
c.
d.
e. none of these
____ 3. Find the standard equation of the sphere with center C and radius r.
C (4, –1, 5); r = 8
a. (x + 4)2 + (y – 1)2 + (z + 5)2 = 64
b. (x + 4)2 + (y – 1)2 + (z + 5)2 = 8
c. (x – 4)2 + (y + 1)2 + (z – 5)2 = 8
d. (x – 4)2 + (y + 1)2 + (z – 5)2 = 64
____ 4. Find the distance from to the xy-planes.
a. 8
b. 16
c. 10
d. 2
e. 4Stewart - Calculus ET 8e Chapter 12 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 5. Find an equation of the sphere with center that touches the xy-plane.
a.
b.
c.
d.
e.
____ 6. Determine whether the given points are collinear.
A (2, 3, 2), B (–4, 0, 5), and C (4, 4, 1)
a. Not collinear b. Collinear
____ 7. Find the midpoint of the line segment joining the given points.
(4, –2, –3) and (6, –4, –1)
a. (5, 3, 2) c. (1, 3, 1)
b. (1, 1, 1) d. (1, 1, 2)
____ 8. Find the center and the radius of the sphere that has the given equation.
+ + – 4x + 8y = 0
a. ( 2, –4, 0), 2 5 c. ( –2, 4, 0), 2 5
b. ( –2, 4, 0), 20 d. ( 2, –4, 0), 20Stewart - Calculus ET 8e Chapter 12 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 9. Plot the given points in a three-dimensional coordinate system.
a. c.
b. d.Stewart - Calculus ET 8e Chapter 12 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 10. Find the unit vectors that are parallel to the tangent line to the curve at the point .
a.
b.
c.
d.
e.
____ 11. Find the work done by a force that moves an object from the point to the
point along a straight line. The distance is measured in meters and the force in newtons.
a.
b.
c.
d.
e.
____ 12. Find the cross product .
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 13. Let and let u be a vector with length that starts at the origin and rotates in the xy - plane.
Find the maximum value of the length of the vector .
a.
b.
c.
d.
e.
____ 14. Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
a.
b.
c.
d.
e. None of these
____ 15. Find correct to three decimal places where , , .
a.
b.
c.
d.
e.
____ 16. Find the distance between the planes.
a.
b. 1
3
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 17. Find, correct to the nearest degree, the angle between the planes.
a.
b.
c.
d.
e. none of these
____ 18. Find parametric equations for the line through the point that is parallel to the plane
and perpendicular to the line
a.
b.
c.
d.
e.
____ 19. Find the distance between the point and the plane Round your answer to
two decimal place.
a.
b.
c.
d.
e.
____ 20. Find an equation for the surface obtained by rotating the parabola about the y-axis.
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form C
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. D
2. E
3. D
4. A
5. D
6. B
7. A
8. A
9. B
10. C
11. A
12. C
13. C
14. D
15. C
16. B
17. A
18. E
19. C
20. DStewart - Calculus ET 8e Chapter 12 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Select the correct answer for each question.
____ 1. Suppose you start at the origin, move along the x-axis a distance of units in the positive direction,
and then move downward a distance of units. What are the coordinates of your position?
a.
b.
c.
d.
e.
____ 2. Find that the midpoint of the line segment from to .
a.
b.
c.
d.
e.
____ 3. Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a
right triangle, both, or neither.
A (–1, 0, 1), B (1, 1, –1), C (1, 1, 1)
a. 3, 2, , right
b. 1, 2, , neither
c. 1, 1, , both
d. 1, 1, , isosceles
____ 4. Find the distance from to the xy-planes.
a. 8
b. 16
c. 10
d. 2
e. 4Stewart - Calculus ET 8e Chapter 12 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 5. Find an equation of the sphere with center that touches the xy-plane.
a.
b.
c.
d.
e.
____ 6. Sketch the plane in a three-dimensional space represented by the equation.
z = –1
a. c.
b. d.Stewart - Calculus ET 8e Chapter 12 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. Determine whether the given points are collinear.
A (2, 3, 2), B (–4, 0, 5), and C (4, 4, 1)
a. Not collinear b. Collinear
____ 8. Find the midpoint of the line segment joining the given points.
(4, –2, –3) and (6, –4, –1)
a. (5, 3, 2) c. (1, 3, 1)
b. (1, 1, 1) d. (1, 1, 2)
____ 9. Find the center and the radius of the sphere that has the given equation.
+ + – 4x + 8y = 0
a. ( 2, –4, 0), 2 5 c. ( –2, 4, 0), 2 5
b. ( –2, 4, 0), 20 d. ( 2, –4, 0), 20
____ 10. Find the work done by a force that moves an object from the point to the
point along a straight line. The distance is measured in meters and the force in newtons.
a.
b.
c.
d.
e.
____ 11. Find the cross product .
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 12. Let and let u be a vector with length that starts at the origin and rotates in the xy - plane.
Find the maximum value of the length of the vector .
a.
b.
c.
d.
e.
____ 13. Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
a.
b.
c.
d.
e. None of these
____ 14. Find an equation of the set of all points equidistant from the points and
a.
b.
c.
d.
e.
____ 15. Find the distance between the planes.
a.
b. 1
3
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 16. Find, correct to the nearest degree, the angle between the planes.
a.
b.
c.
d.
e. none of these
____ 17. Which of the given lines is parallel to the line
a.
b.
c.
d.
e.
____ 18. Find the distance between the point and the plane Round your answer to
two decimal place.
a.
b.
c.
d.
e.
____ 19. Find an equation for the surface consisting of all points P for which the distance from P to the x-axis
is times the distance from P to the yz-plane.
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 20. Reduce the equation to one of the standard forms.
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form D
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. D
2. C
3. A
4. A
5. D
6. A
7. B
8. A
9. A
10. A
11. C
12. C
13. D
14. B
15. B
16. A
17. E
18. C
19. B
20. EStewart - Calculus ET 8e Chapter 12 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1. Find that the midpoint of the line segment from to .
____ 2. Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a
right triangle, both, or neither. Select the correct answer.
A (–1, 0, 1), B (1, 1, –1), C (1, 1, 1)
a. 1, 2, , neither
b. 1, 1, , isosceles
c. 1, 1, , both
d. 3, 2, , right
3. Find the distance from to the xy-planes.
4. Sketch the plane in a three-dimensional space represented by the equation.
z = –1
____ 5. Find the midpoint of the line segment joining the given points. Select the correct answer.
(3, 1, 4) and (5, –1, 6)
a. (1, 0, 1) c. (4, 0, 5)
b. (1, 1, 1) d. (1, 1, 5)
6. Find the center and the radius of the sphere that has the given equation.
+ + – 6x + 10y = 0
7. Find the unit vectors that are parallel to the tangent line to the curve at the point .
____ 8. Find the work done by a force that moves an object from the point to the
point along a straight line. The distance is measured in meters and the force in newtons.
Select the correct answer.
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
9. Calculate the angle between a and b (correct to the nearest degree).
10. Find the cross product .
____ 11. Let and let u be a vector with length that starts at the origin and rotates in the xy - plane.
Find the maximum value of the length of the vector . Select the correct answer.
a.
b.
c.
d.
e.
12. Find correct to three decimal places where , , .
13. Find an equation of the set of all points equidistant from the points and
14. Find, correct to the nearest degree, the angle between the planes.
____ 15. Find the point at which the line given by the parametric equations below intersects the plane.
Select the correct answer.
a.
b.
c.
d.
e.
16. Find the distance (correct to two decimal places) between the given parallel planes.Stewart - Calculus ET 8e Chapter 12 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 17. Find parametric equations for the line through the point that is parallel to the plane
and perpendicular to the line
Select the correct answer.
a.
b.
c.
d.
e.
18. Find an equation for the surface consisting of all points that are equidistant from the point
and the plane .
19. Find an equation for the surface obtained by rotating the parabola about the y-axis.
____ 20. Classify the surface.
Select the correct answer.
a. A hyperboloid of one sheet with center and axis parallel to the z-axis.
b. A circular paraboloid with vertex and axis the z-axis.
c. A cone with axis parallel to the z-axis and vertex .Stewart - Calculus ET 8e Chapter 12 Form E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1.
2. D
3. 8
4.
5. C
6. ( 3, –5, 0), 34
7.
8. E
9.
10.
11. D
12.
13.
14.
15. E
16.
17. A
18.
19.
20. CStewart - Calculus ET 8e Chapter 12 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 1. Find the distance from to the xy-planes. Select the correct answer.
a. 8
b. 16
c. 10
d. 2
e. 4
2. Sketch the plane in a three-dimensional space represented by the equation.
z = –1
____ 3. Find the center and the radius of the sphere that has the given equation. Select the correct answer.
+ + – 4x + 8y = 0
a. ( 2, –4, 0), 2 5 c. ( –2, 4, 0), 2 5
b. ( –2, 4, 0), 20 d. ( 2, –4, 0), 20
4. Two forces with magnitudes 8 lb and 12 lb act on an object at a point P as shown in the
figure. Find the magnitude of the resultant force F acting at P. Round the result to the nearest tenth.
5. Find the unit vectors that are parallel to the tangent line to the curve at the point .
____ 6. Find the values of x such that the vectors and are orthogonal.
Select the correct answer.
a.
b.
c.
d.
e.Stewart - Calculus ET 8e Chapter 12 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. Find the work done by a force that moves an object from the point to the
point along a straight line. The distance is measured in meters and the force in newtons.
Select the correct answer.
a.
b.
c.
d.
e.
____ 8. Calculate the angle between a and b (correct to the nearest degree).
Select the correct answer.
a.
b.
c.
d.
e. None of these
9. Let and let u be a vector with length that starts at the origin and rotates in the xy - plane.
Find the maximum value of the length of the vector .
10. Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
11. Find the distance between the planes.
____ 12. Find, correct to the nearest degree, the angle between the planes. Select the correct answer.
a.
b.
c.
d.
e. none of theseStewart - Calculus ET 8e Chapter 12 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 13. Find the point at which the line given by the parametric equations below intersects the plane.
Select the correct answer.
a.
b.
c.
d.
e.
____ 14. Find the distance (correct to two decimal places) between the given parallel planes.
Select the correct answer.
a.
b.
c.
d.
e.
15. Find parametric equations for the line through the point that is parallel to the plane
and perpendicular to the line
16. Find an equation of the plane with x-intercept , y-intercept and z-intercept .
____ 17. Find the distance between the point and the plane Round your answer to
two decimal place.
Select the correct answer.
a.
b.
c.
d.
e.
18. Find an equation for the surface consisting of all points that are equidistant from the point
and the plane .
19. Find an equation for the surface obtained by rotating the parabola about the y-axis.Stewart - Calculus ET 8e Chapter 12 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
20. Classify the surface.Stewart - Calculus ET 8e Chapter 12 Form F
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. A
2.
3. A
4.
5.
6. E
7. A
8. B
9.
10.
11. 1
3
12. A
13. E
14. D
15.
16.
17. C
18.
19.
20. A cone with axis parallel to the z-axis and vertex .Stewart - Calculus ET 8e Chapter 12 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 1. Find the center and radius of the sphere. Select the correct answer.
a.
b.
c.
d.
e. none of these
2. Sketch the plane in a three-dimensional space represented by the equation.
z = 2
____ 3. Determine whether the given points are collinear. Select the correct answer.
A (0, 1, 0), B (–6, –2, 3), and C (–2, –2, –1)
a. Collinear b. Not collinear
4. Find the center and the radius of the sphere that has the given equation.
+ + – 2x + 6y = 0
5. Find the unit vectors that are parallel to the tangent line to the curve at the point .
____ 6. Find the values of x such that the vectors and are orthogonal.
Select the correct answer.
a.
b.
c.
d.
e.
7. Find the work done by a force that moves an object from the point to the
point along a straight line. The distance is measured in meters and the force in newtons.Stewart - Calculus ET 8e Chapter 12 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 8. Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
Select the correct answer.
a.
b.
c.
d.
e. None of these
9. Find correct to three decimal places where , , .
____ 10. Find an equation of the set of all points equidistant from the points and
Select the correct answer.
a.
b.
c.
d.
e.
11. Find the distance between the planes.
____ 12. Identify the planes that are perpendicular. Select the correct answer.
a.
b.
c.
d.
e.
____ 13. Find, correct to the nearest degree, the angle between the planes. Select the correct answer.
a.
b.
c.
d.
e. none of theseStewart - Calculus ET 8e Chapter 12 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
14. Find the point at which the line given by the parametric equations below intersects the plane.
____ 15. Find the distance (correct to two decimal places) between the given parallel planes.
Select the correct answer.
a.
b.
c.
d.
e.
16. Which of the given lines is parallel to the line
____ 17. Find an equation for the surface consisting of all points P for which the distance from P to the x-axis
is times the distance from P to the yz-plane. Select the correct answer.
a.
b.
c.
d.
e.
18. An ellipsoid is created by rotating the ellipse about the x-axis. Find the equation of the
ellipsoid.
____ 19. Classify the surface. Select the correct answer.
a. A hyperboloid of one sheet with center and axis parallel to the z-axis.
b. A cone with axis parallel to the z-axis and vertex .
c. A circular paraboloid with vertex and axis the z-axis.
20. Reduce the equation to one of the standard forms.Stewart - Calculus ET 8e Chapter 12 Form G
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. E
2.
3. B
4. ( 1, –3, 0), 10
5.
6. A
7.
8. D
9.
10. A
11. 4
15
12. A
13. A
14.
15. A
16.
17. B
18.
19. B
20.Stewart – Calculus ET 8e Chapter 12 Form H
© 2016 Cengage etLearning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 1. Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle, a
right triangle, both, or neither. Select the correct answer.
A (–1, 0, 1), B (1, 1, –1), C (1, 1, 1)
a. 1, 1, , isosceles
b. 1, 1, , both
c. 3, 2, , right
d. 1, 2, , neither
2. Find the standard equation of the sphere with center C and radius r.
C (4, –1, 1); r = 6
____ 3. Find the distance from to the xy-planes. Select the correct answer.
a. 8
b. 16
c. 10
d. 2
e. 4
4. Find an equation of the sphere with center that touches the xy-plane.
____ 5. Find the midpoint of the line segment joining the given points. Select the correct answer.
(0, –1, –3) and (2, –3, –1)
a. (1, 2, 1) c. (1, 1, 1)
b. (1, 1, 2) d. (1, 2, 2)
6. Find the center and the radius of the sphere that has the given equation.
+ + – 10x + 4y = 0Stewart – Calculus ET 8e Chapter 12 Form H
© 2016 Cengage etLearning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 7. Find the work done by a force that moves an object from the point to the
point along a straight line. The distance is measured in meters and the force in newtons.
Select the correct answer.
a.
b.
c.
d.
e.
8. Calculate the angle between a and b (correct to the nearest degree).
9. Find the cross product .
10. Find the distance between the planes.
____ 11. Identify the planes that are perpendicular. Select the correct answer.
a.
b.
c.
d.
e.
____ 12. Find, correct to the nearest degree, the angle between the planes. Select the correct answer.
a.
b.
c.
d.
e. none of theseStewart – Calculus ET 8e Chapter 12 Form H
© 2016 Cengage etLearning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
13. Find the distance (correct to two decimal places) between the given parallel planes.
____ 14. Find parametric equations for the line through the point that is parallel to the plane
and perpendicular to the line
Select the correct answer.
a.
b.
c.
d.
e.
15. Find an equation of the plane with x-intercept , y-intercept and z-intercept .
____ 16. Find an equation for the surface consisting of all points that are equidistant from the point
and the plane .
Select the correct answer.
a.
b.
c.
d.
e.
17. Find an equation for the surface consisting of all points P for which the distance from P to the x-axis
is times the distance from P to the yz-plane.
18. An ellipsoid is created by rotating the ellipse about the x-axis. Find the equation of the
ellipsoid.Stewart – Calculus ET 8e Chapter 12 Form H
© 2016 Cengage etLearning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
____ 19. Find an equation for the surface obtained by rotating the parabola about the y-axis.
Select the correct answer.
a.
b.
c.
d.
e.
20. Reduce the equation to one of the standard forms.Stewart – Calculus ET 8e Chapter 12 Form H
© 2016 Cengage etLearning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Answer Key
1. C
2. (x – 4)2 + (y + 1)2 + (z – 1)2 = 36
3. A
4.
5. D
6. ( 5, –2, 0), 29
7. B
8.
9.
10. 1
3
11. B
12. A
13.
14. D
15.
16. C
17.
18.
19. B
20.
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