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Vectors And Cartesian Three-Space Practice Test

By — McGraw-Hill Professional
Updated on Oct 3, 2011

If necessary, review:

Vectors and Catesian Three-Space Practice Test

Directions: A good score is eight correct.

1. The dot product (3,5,0) • (−4,−6,2) is equal to

(a) the scalar quantity −4

(b) the vector (−12,−30,0)

(c) the scalar quantity −42

(d) a vector perpendicular to the plane containing them both

2. What does the graph of the equation y = 3 look like in Cartesian three-space?

(a) A plane perpendicular to the y axis

(b) A plane parallel to the xy plane

(c) A line parallel to the y axis

(d) A line parallel to the xy plane

3. Suppose vector d in the Cartesian plane begins at exactly (1,1) and ends at exactly (4,0). What is dir d , expressed to the nearest degree?

(a) 342°

(b) 18°

(c) 0°

(d) 90°

4. Suppose a line is represented by the equation ( x − 3)/2 = ( y + 4)/5 = z − 1. Which of the following is a point on this line?

(a) (−3,4,−1)

(b) (3,−4,1)

(c) (2,5,1)

(d) There is no way to determine such a point without more information

5. Let Δ PQR be a right triangle whose hypotenuse measures exactly 1 unit in length, and whose other two sides measure p meters and q meters, as shown in Fig. 9-14. Let θ be the angle whose apex is point P . Which of the following statements is true?

(a) sin θ = p/q

(b) sin θ = cos φ

(c) tan φ = tan θ

(d) cos θ = 1/(tan φ )

Vectors and Cartesian Three-Space Quiz

Fig. 9-14 . Illustration for quiz questions 5 and 6.

6. With reference to Fig. 9-14, the Pythagorean theorem can be used to demonstrate that

(a) sin θ + cos φ = 1

(b) tan θ − tan φ = 1

(c) (sin θ ) 2 + (cos θ ) 2 = 1

(d) (sin θ ) 2 − (cos θ ) 2 = 1

7. What is the cross product (2 i + 0 j + 0 k ) × (0 i + 2 j + 0 k )?

(a) 0 i + 0 j + 0 k

(b) 2 i + 2 j + 0 k

(c) 0 i + 0 j + 4 k

(d) The scalar 0

8. What is the sum of the two vectors (3,5) and (−5,−3)?

(a) (0,0)

(b) (8,8)

(c) (2,2)

(d) (−2,2)

9. If a straight line in Cartesian three-space has direction defined by m = 0 i + 0 j + 3 k , we can surmise

(a) that the line is parallel to the x axis

(b) that the line lies in the yz plane

(c) that the line lies in the xy plane

(d) none of the above

10. Suppose a plane passes through the origin, and a vector normal to the plane is represented by 4 i − 5 j + 8 k . The equation of this plane is

(a) 4 x − 5 y + 8 z = 0

(b) −4 x + 5 y − 8 z = 7

(c) ( x − 4) = ( y + 5) = ( z − 8)

(d) impossible to determine without more information

Answers:

1. c

2. a

3. a

4. b

5. b

6. c

7. c

8. d

9. d

10. a

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