Name:    Chapter 11 Post Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Find the distance between the points.

 a. units b. units c. units d. units e. units

2.

Find the distance between the points.

 a. units b. units c. units d. units e. units

3.

Find the lengths of the sides of the triangle with the indicated vertices.

 a. , , b. , , c. , , d. , , e. , ,

4.

Find the standard form of the equation of the sphere with the given characteristics.

Center: ; diameter:
 a. b. c. d. e.

5.

Find the vector z, given .

 a. b. c. d. e.

6.

Find the vector z, given .

 a. b. c. d. e.

7.

Find the magnitude of v.

 a. b. c. d. e.

8.

Find the angle between the vectors u and v. Express your answer in degrees and round to the nearest tenth of a degree.
u = –2i –3j –3kv = –2i –2j –7k
 a. 41.2° b. 61.1° c. 48.8° d. 28.9° e. 90°

9.

Determine whether u and v are parallel, orthogonal, or neither.
u = , v =
 a. neither b. parallel c. orthogonal

10.

Use the vectors u and v to find .

 a. b. c. d. e.

11.

Find the area of the parallelogram that has the vectors as adjacent sides.

 a. square units b. square units c. square units d. square units e. square units

12.

Find the area of the parallelogram that has the vectors as adjacent sides.

 a. square units b. square units c. square units d. square units e. square units

13.

Find the area of the parallelogram that has the vectors as adjacent sides.

 a. square units b. square units c. square units d. square units e. square units

14.

Find the triple scalar product.

 a. b. c. d. e.

15.

Find and show that it is orthogonal to both u and v.

 a. b. c. d. e.

16.

Find the area.

 a. square units b. square units c. square units d. square units e. square units

17.

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line.

Point:
Parallel to:
 a. Symmetric equations: b. Symmetric equations: c. Symmetric equations: d. Symmetric equations: e. Symmetric equations:

18.

Find a set of symmetric equations of the line that passes through the given points.

 a. b. c. d. e.

19.

Find a set of parametric equations of the line.

Passes through and is perpendicular to .
 a. b. c. d. e.

20.

Find a set of parametric equations of the line.

Passes through  and is parallel to .
 a. b. c. d. e.