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1. When a vector is multiplied by a negative scalar ____.
A. its direction changes.
B. its magnitude changes.
C. both magnitude and direction change.
D. neither magnitude nor direction changes.
2. When a vector is multiplied by a scalar, the product is
A. always a vector.
B. always a scalar.
C. may be a scalar or a vector.
D. neither a scalar nor a vector.
3. Given a = b . This means that vectors a and b
A. have equal magnitudes and are in opposite directions.
B. have unequal magnitudes and are in the same direction.
C. are orthogonal vectors with equal magnitudes.
D. have equal magnitudes and are in the same direction.
4. If u = 3i + 3 j + 3k and v = 4i + 2 j + 6k , find projv u .
9
9
12
12
A. (3i + 3 j + 3k ) B. (2i + j + 3k ) C.
(2i + j + 3k ) D.
(3i + 3 j + 3k )
7
7
7
7
5. Two vectors are given as follows: a = −2i − 5 j + 2k , b = −5i − 2 j − 3k . Find the magnitude
of the following vector a × b
A. 12 B. 18 C. 26 D. 31
6. Given a = 2,0,1 and b = 4,1, 2 , what is the area of the parallelogram spanned by the
vectors a and b ?
A. 3 2 B. 2 3 C. 5 D. 2 5
7. Find the work done by the force F = 7i + 2 j + 5k in moving an object from the point
A(4, 5, 3) to the point B(8, 10, -2). (Assume the unit of length is meters and the magnitude
of the force is measured in newtons.)
A . 63 J B. 36 J C. 13 J D. − 36 J
8. If a = 2i + j + 2k and b = 5i − 3j + k , the vector (orthogonal) projection of a onto b is
9(5i − 3j + k )
5i − 3j + k
A.
B.
C. 9(5i − 3j + k ) D. 5i − 3j + k
35
35
9. Find the angle between the two vectors given by a = 3 j − 3k and b = −2i + 2 j − k .
π
π
π
π
A.
B.
C.
D.
6
4
3
2
10. The value of sine of the angle between the vectors i − 2 j + 3k and 2i + j + k is
5
5
5
5
A.
B.
C.
D.
21
7
14
2 7


11. The volume of the parallelepiped whose sides are given by OA = 2i − 3j , OB = i + j − k ,

OC = 3i − k , is
4
2
A.
B. 4 C.
D. none of these
13
7
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