Stewart – Calculus ET 8e Chapter 12 Form D
____ 20. Reduce the equation to one of the standard forms.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 12 Form D
Answer Key
Stewart – Calculus ET 8e Chapter 12 Form E
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
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
____ 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
Answer Key
Stewart – Calculus ET 8e Chapter 12 Form F
____ 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),
25
c. ( –2, 4, 0),
25
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
____ 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 these
Stewart – Calculus ET 8e Chapter 12 Form F
____ 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
20. Classify the surface.
Stewart – Calculus ET 8e Chapter 12 Form F
Answer Key
Stewart – Calculus ET 8e Chapter 12 Form G
____ 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
____ 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 these
Stewart – Calculus ET 8e Chapter 12 Form G
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
Answer Key
Stewart – Calculus ET 8e Chapter 12 Form H
____ 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 = 0
Stewart – Calculus ET 8e Chapter 12 Form H
____ 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 these
Stewart – Calculus ET 8e Chapter 12 Form H
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
____ 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
Answer Key