Vectors:
1) The components of vector A are given as follows:
Ax = 8
Ay = 6
The magnitude of A is closest to:
A) 48
B) 14
C) 10
D) 15
E) 12
2) The components of vector A are given as follows:
Ax = -9
Ay = 3
The angle measured counter-clockwise from the x-axis to vector A, in
degrees, is closest to:
A) 339
B) 288
C) 120
D) 28
E) 159
3) The components of vector A and B are given as follows:
Ax = -1
Ay = -8
Bx = -13
By = -3
The magnitude of B – A, is closest to:
A) 10.7
B) 11
C) 17.8
D) 13
E) 25
4) The magnitude of B is 10. Vector B lies in the 4th quadrant and forms a 53
with the x-axis. (sin 53 = .8 & cos 53 = .6) The components of Bx and By are:
A) Bx = -6, By = -8
B) Bx = -6, By = 8
C) Bx = 8, By = -26
D) Bx = 6, By = -8
Figure 1.1
Vectors A and B are shown. Vector C is given by C = A + B
Y
4.5
𝐴
30°
60°
6
X
𝐵
3
0

5) In the figure above, the magnitude of C is closest to:
A) 7.5
B) 3.9
C) 5.2
D) 9.3
E) 2.6
6) Which of the following is a true statement?
A) It is possible to add a scalar quantity to a vector.
B) The magnitude of a vector can be zero even though one of its
components is not zero.
C) The sum of the magnitudes of two unequal vectors can be zero.
D) Rotating a vector about an axis passing through the tip of the vector
does not change the vector.
E) Vectors must be added geometrically.
7) What is the magnitude of the sum of the following vectors?
X = 2i + 9j – 13k
Y = -i – 4j +2k
Z = i + 5j
A) 9.3
B) 12.3
C) 15
D) 10.7
E) 17
8) Two vectors are given:
A = -3i + 6j – 4k
B = -5i – 2j – 2k
The angle between vectors A and B, in degrees, is:
A) 117
B) 76
C) 150
D) 29
9) Two vectors are given:
X = -2i - 5j + 2k
The magnitude of |X x Y| is:
A) 33
B) 29
E) 161
Y = -5i – 2j – 3k
C) 25
D) 21
E) 17
Figure 1.2
𝐴
𝐵
7
4
𝐶
6
65° 45°
10)In Figure 1.2, the scalar product B  C is:
A) 0
B) 17
C) 24
D) -17
E) -24
11)In Figure 1.2, the scalar product of A  C is:
A) 0
B) 14
C) 42
D) -14
E) -42
12)In Figure 1.2, the magnitude of the vector product A x B is:
A) 12
B) 30
C) 25
D) 20
E) 10
13)In figure 1.2, the magnitude and direction of vector product C x A are:
A) 14, directed out of the plane
B) 39, directed out of the plane
C) 39, directed into the plane
D) 14, directed on the plane
E) 14, directed into the plane
14)A boat undergoes the following displacements: First, it travels 70 m in a
direction 30 north of east. Next, it travels 85 m due south. Finally, it goes
120 m 60 west of north. Determine how far the boat ends up from its
starting point.
A) 44.4
B) 45.1
C) 48
D) -39.3
E) 47.5
15)Which of the following is an accurate statement?
A) If the vectors A and B are each rotated through the same angle about
the same axis, the product A  B will be unchanged
B) If the vectors A and B are each rotated through the same angle about
the same axis, the product A x B will be unchanged
C) If a vector A is rotated about an axis parallel to vector B, the product
A  B will be changed
D) When a scalar quantity is added to a vector, the result is a vector of
larger-magnitude than the original vector.
16)Vector A has a magnitude of 40 and makes a 60 angle with the y-axis. Vector
B has a magnitude of 40 and makes a 30 angle with the x-axis. If vector A is
in quadrant I and vector B is in quadrant II, what is the magnitude of the sum
of the two vectors?
A) 20
B) 40
C) 60
D) 80
E) 100
17) Vector A has a magnitude of 20 and makes a 45 angle with the y-axis. Vector
B has a magnitude of 10 and makes a 60 angle with the x-axis. If vector A is
in quadrant III and vector B is in quadrant I, what is the magnitude of the
sum of the two vectors?
A) 15
B)30.4
C) 10.6
D) 13.9
E) 27
18)A vector is given:
A = 3i – 2j -2k
The angle between vector A and the y-axis, in degrees, is closest to:
A) 119
B) 61
C) 29
D) 151
Problems 19 - 20
𝐴
(A)
𝐵
(B)
(D)
19)What is the difference of vector A and vector B? 𝐴 - 𝐵
(A) A
(B) B
(C) C
(D) D
(C)
(E)
(E) E
20) To satisfy this equation:
𝐴+ 𝐵+ 𝐶 =0
Vector C would represent:
(A) A
(B) B
(C) C
(D) D
(E) E
E) 90
Answer Key:
1) C
2) E
3) D
4) D
5) A
6) E
7) C
8) B
9) A
10)B
11)D
12)C
13)B
14)A
15)A
16)B
17)C
18)A
19)A
20) D