Practice Problems
Vector Addition
Directions:
On this worksheet you will practice adding vectors. Remember that vectors are added graphically by using the
headtotail method
and that the resultant is the vector that connects the beginning of the first vector to the end of the final vector. You will be asked questions regarding each resultant's magnitude and direction. The example vectors displayed in the table below are not drawn to scale; however, they do indicate correct relative directions.
x
b
a
z
omit
Question 1
Given the vectors:
x
= (12 meters, 0º) and
z
= (5 meters, 0º).
What is the magnitude, or length, of
R
_{1}
=
x
+ 4
z
?
8 meters
53 meters
68 meters
32 meters
omit
Question 2
What is the magnitude, or length, of
R
_{2}
= 4
x

z
?
NOTE: subtracting a vector means that you should add a vector that has the same magnitude, but points in 180º the opposite direction.
53 meters
28 meters
43 meters
8 meters
omit
Question 3
What is the direction of
R
_{3}
if
R
_{3}
=
 R
_{2}
225º
0º
180º
270º
omit
Question 4
Given the vectors:
x
= (12 meters, 0º) and
a
= (7 meters, 35º)
What is the magnitude, or length, of
R
_{4}
=
x
+ 4
a
?
38.5 meters
40.0 meters
36.2 meters
55.0 meters
omit
Question 5
What is the direction of
R
_{4}
in degrees?
32.0º
24.7º
39.3º
10.3º
omit
Question 6
Given the vectors:
a
= (7 meters, 35º) and
b
= (23 meters, 90º)
What is the magnitude, or length, of
R
_{5}
= 4
a
 4
b
120.0 meters
53.0 meters
70.9 meters
79.3 meters
omit
Question 7
What is the direction of
R
_{5}
in degrees?
286.8º
106.8º
343.2º
16.8º
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