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. 4

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.

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

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. E

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