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.


Correct answer : (4)
 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.


Correct answer : (1)
 3.  
The resultant vector of PQ + 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.


Correct answer : (4)
 4.  
The resultant vector of A + 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.


Correct answer : (2)
 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.


Correct answer : (4)
 6.  
If S has a magnitude of 18 and a direction of 225° then the x and y - components of 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.


Correct answer : (1)
 7.  
Use the vectors in the figure to find the resultant of A + B - 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.


Correct answer : (4)
 8.  
If PQ has a magnitude of 4 and a direction of 70° then, the x and y-components of 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.


Correct answer : (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.


Correct answer : (3)
 10.  
If AB has a magnitude of 12 and a direction of 105° then the x and y - components of 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.


Correct answer : (3)

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