Vectors and Dot Product
Find a· b.
1) a = 2, 4 , b = 2, 5
A) 4, 20
B) 4, 9
C) 16
D) 24
2) a = 3, -1 , b = -3, 1
A) -9, -1
B) 0, 0
C) -10
D) 8
3) a = 5, -10 , b = 6, 5
A) 11, -5
B) 80
C) 30, -50
D) -20
4) a = 4, -6 , b = 5, -7
A) 62
B) 22
C) 9, -13
D) 20, 42
5) a = -1, -1 , b = -3.5, 2
A) -4.5, 1
B) 5.5
C) 3.5, -2
D) 1.5
6) a = 7i - 4j, b = 4i + 3j
A) 11, -1
B) -40
C) 16
D) 28, -12
7) a = 4i + 8j, b = -2i + 3j
A) -8, 24
B) 2, 11
C) 32
D) 16
8) a = 6j, b = i + 4j
A) 0, 24
B) 1, 24
C) 24
D) -24
B) 4 3
C) 6
D) 5 2
10) v = -7, 3
A) 58
B) 10
C) 2i 10
D) -4
11) v = 5j
A) 25
B) 5
C) -5
D) 0
12) v = 6, 8
A) 14
B) 10
C) -2
D) 100
Use the dot product to find v .
9) v = 1, 7
A) 8
Find the angle between the given vectors to the nearest tenth of a degree.
13) u = -5, 8 , v = -4, 8
A) -7.3°
B) 2.7°
C) 5.4°
14) u = -2, -1 , v = 5, -9
A) 102.5°
B) 46.3°
C) 92.5°
D) 15.4°
D) 36.3°
PreCalculus
15) u = 5i - 9j, v = 5i + j
A) 65.9°
B) 90.4°
C) 100.1°
D) 45.2°
16) u = i + 7j, v = -i + 8j
A) 13.6°
B) 68.9°
C) 27.8°
D) 15.3°
17) u = 4, -3 , v = -6, -8
A) 90°
B) 45°
C) 180°
D) 0°
C) 210°
D) 240°
18) u = 5 cos π
π
4π
4π
i + 5 sin j, v = cos i + sin j
6
6
3
3
A) 120°
B) 150°
Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, projvu .
19) u = 8, 6 , v = 2, 4
A) 2, 4 + 6, 2
B) 3, 6 + 5, -2.5
C) 4, 8 + 4, -2
D) -1, -2 + 9, -4.5
20) u = 5, -5 , v = 6, 8
A) 3, 4 + -8, 6
C) 1.5, 2 + 3.5, -7
B) -0.6, -0.8 + 5.6, -4.2
D) 6, 8 + -1, -13
21) u = -3, -3 , v = -9, -3
A) 3, 1 + -6, -4
C) -3.6, -1.2 + 0.6, -1.8
B) -6, -2 + 3, -9
D) -9, -3 + 6, 0
Determine whether the vectors u and v are parallel, orthogonal, or neither.
22) u = 10, 0 , v = 0, -9
A) Orthogonal
B) Neither
C) Parallel
23) u = 3, 0 , v = 0, -3
A) Neither
B) Parallel
C) Orthogonal
24) u = 6, -2 , v = 8, 24
A) Parallel
B) Orthogonal
C) Neither
25) u = 7, 2 , v = 21, 6
A) Neither
B) Parallel
C) Orthogonal
26) u = 8, 4 , v = 10, 7
A) Parallel
B) Neither
C) Orthogonal
Solve the problem.
27) What is the minimum force required to prevent a ball weighing 24.0 lb from rolling down a ramp which is
inclined 27.2° with the horizontal?
A) 11 lb
B) 10.7 lb
C) 5.5 lb
D) 21.3 lb
Calin M. Agut - 2012
PreCalculus
28) A constant force F = 16, 31 moves an object along a vector D = 10, 2 , where units are in pounds and feet.
Find the work done.
A) 98 foot-pounds
B) -98 foot-pounds
C) 355.8 foot-pounds
D) 222 foot-pounds
29) A constant force F = 41i + 25j moves an object along a vector D = 19i - 12j, where units are in pounds and feet.
Find the work done.
A) 479 foot-pounds
B) -1079 foot-pounds
C) 1079 foot-pounds
D) 1079.1 foot-pounds
30) Find the work done by a force F of 10 pounds acting in the direction 2, 5 in moving an object 6 feet from (0, 0)
to (6, 0).
A) ≈ 31.57 foot-pounds
B) ≈ 120 foot-pounds
C) ≈ 22.28 foot-pounds
D) ≈ 55.71 foot-pounds
Calin M. Agut - 2012
Answer Key
Testname: 4_DOT_PRODUCT
1) D
2) C
3) D
4) A
5) D
6) C
7) D
8) C
9) D
10) A
11) B
12) B
13) C
14) C
15) C
16) C
17) A
18) B
19) C
20) B
21) C
22) A
23) C
24) B
25) B
26) B
27) A
28) D
29) A
30) C
Calin M. Agut - 2012