# Vector Operation Worksheet

Vector Operation Worksheet
• Page 1
1.
Two vectors are equivalent if ______
 a. they have same direction. b. they have same length but their directions are opposite. c. they have same length. d. they have same length and direction.

#### Solution:

Two vectors are equivalent if they have same length and direction.

2.
Two vectors are said to be opposite if ______
 a. they have same length but their directions are opposite. b. they have different lengths. c. they have same length. d. they have same length and same direction.

#### Solution:

Two vectors are said to be opposite if they have same length but their directions are opposite.

3.
The resultant vector of $\stackrel{\to }{\text{PQ}}$ + $\stackrel{\to }{\text{PR}}$ is _________ .

 a. Figure 4 b. Figure 2 c. Figure 3 d. Figure 1

#### Solution:

Using PQ and PR as adjacent sides, complete the parallelogram.

The resultant vector is the diagonal whose initial point is P, which is shown in figure 1.

4.
The resultant vector of $\stackrel{\to }{\text{A}}$ + $\stackrel{\to }{\text{B}}$ is ________ .

 a. Figure 4 b. Figure 2 c. Figure 3 d. Figure 1

#### Solution:

Move vector B parallel to its original directions and complete the triangle by joining the tail of A to the head of B, which is the resultant vector.

5.
A vector quantity has _________ .
 a. Magnitude b. Direction c. Magnitude and not direction d. Both magnitude and direction

#### Solution:

Any quantity that has both magnitude and direction is called a vector quantity.

6.
If $\stackrel{\to }{\text{S}}$ has a magnitude of 18 and a direction of 225° then the $x$ and $y$ - components of $\stackrel{\to }{\text{S}}$ to the nearest integer are _______ .
 a. -13, -13 b. -13, 13 c. 13, 13 d. 13, -3

#### Solution:

x - component = r cos θ

x = 18 cos 225°

x = -12.727922

y-component = r sin θ

y = 18 sin 225°

y = -12.727922

To the nearest integer, the x - component is -13 and the y - component is -13.

7.
Use the vectors in the figure to find the resultant of $\stackrel{\to }{\text{A}}$ + $\stackrel{\to }{\text{B}}$ - $\stackrel{\to }{\text{C}}$.

 a. Figure 4 b. Figure 1 c. Figure 2 d. Figure 3

#### Solution:

To get the resultant vector, connect the tail of one vector to the head of the other.

8.
If $\stackrel{\to }{\text{PQ}}$ has a magnitude of 4 and a direction of 70° then, the $x$ and $y$-components of $\stackrel{\to }{\text{PQ}}$ to the nearest integer are ______ .
 a. -1, 4 b. 4, 1 c. 1, 1 d. 1, 4

#### Solution:

x - component = r cos θ

x = 4 cos 70°
[r = 4; θ = 70°.]

x = 1.36808

y - component = r sin θ

y = 4 sin 70°
[r = 4; θ = 70°.]

y = 3.75877

To the nearest interger, the x - component is 1 and the y - component is 4.

9.
A vector quantity is represented by ______ .
 a. A segment b. A curve c. A directed line segment d. A line

#### Solution:

A vector quantity is represented by a direct line segment (or) arrow.

10.
If $\stackrel{\to }{\text{AB}}$ has a magnitude of 12 and a direction of 105° then the $x$ and $y$ - components of $\stackrel{\to }{\text{AB}}$ to the nearest integer are ______ .
 a. 3, 12 b. -3, -12 c. -3, 12 d. 3, -12

#### Solution:

x - component = r cos θ

x = 12 cos 105°
[r = 12; θ = 105°.]

x = -3.105828

y - component = r sin θ

y = 12 sin 105°

y = 11.5911099

To the nearest interger, the x-component is - 3 and the y-component is 12.