Try these Review Questions: Answers
1. Given the points A(-2, 0, 7) and B(-1, 2, 4) , AB is:
(a) (-3, 2,11)
(b) (2, 0, 28)
(c) (-1, -2, 3)
(d) (1, 2, -3)
2. Given the vectors OC = (4, 2, 8) and OD = (0,1,-3), CD is:
(a) 9.2
(b) 10
(c) 11.7
(d) 138
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3. The unit vector parallel to vector a  (6 , 8) is:
(a) (24, -32)
(b) (-60, 80)
(c) (6, -8)
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(d) (-0.6, 0.8)
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4. Given the vectors a = (3, -7, 1) and b = (-5, 9, 0) , find a  b
(a) (-15, -63, 0)
(b) (8, -16, 1)
(c) -78
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(d) -23
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5. For any vector u , u u 
(b) u
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
2
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(a) u 2
(d) 0
(c) 2u
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6. For any vector u , u  u 
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

2
(a) u 2
(b) u
(d) 0
(c) 2u
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7. The angle between vectors u =(1, 3, -7) and v =(2, -3, 4) is
(a) 32°
(b) 74°
(c) 76°
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(d) 148°
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8. Given a = (1, 2, 5) and b =(6, 0, 3), a  b =
(a) (2, 9, -4)
(b) (6, 27, -12)
(c) (-2, -9, 4)
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(d) 21
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9. Given c = (4, 9) and d =(3, -1), the scalar projection of c on d is:
(a) 0.30
(b) 0.949
(c) (0.9, 0.3)
(d) (0.12, 0.28)
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
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10. Is the expression c  d  a  b , a vector, scalar or meaningless:
(a) vector
(b) scalar
(c) meaningless
Meaningless because the dot product in the middle is a scalar, and you
cannot “cross” a vector with a scalar.
11. The following points are 3 of the 4 vertices of a parallelogram, F(3, 2, 1), G( 9,8,-1) and
H(-2, -1, 0). The coordinates of the fourth vertex, point E are:
(a) (-8, -7, 2)
(b) (8, 7, -2)
(c) (3, 8, 5)
(d) (-3, -8, -5)
Sketch it out in sequence E F G H. Vector “FE” must equal vector “GH”
Vector GH = (-11,-9,1). Vector FE = (x – 3, y – 2, z – 1). If these vectors are
equal, then x – 3 = -11; y – 2 = -9; and z – 1 = 1; so x=-8; y=-7; and z=2.
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12. What is k  i ?

   
 
(b) a  b 

 
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2
(d) k
(c) j
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13. The simplified form of a  b  a  b is:
(a) a  b
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(b)  i
(a) i
2
* same result as question #5.
 
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(c) 2 a  b
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(d) 0