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
= (3 meters, 0º).
What is the magnitude, or length, of
R
_{1}
=
x
+ 4
z
?
51 meters
24 meters
60 meters
0 meters
omit
Question 2
What is the magnitude, or length, of
R
_{2}
= 3
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.
27 meters
39 meters
33 meters
3 meters
omit
Question 3
What is the direction of
R
_{3}
if
R
_{3}
=
 R
_{2}
180º
270º
225º
0º
omit
Question 4
Given the vectors:
x
= (12 meters, 0º) and
a
= (11 meters, 40º)
What is the magnitude, or length, of
R
_{4}
=
x
+ 3
a
?
41.7 meters
45.0 meters
47.0 meters
42.9 meters
omit
Question 5
What is the direction of
R
_{4}
in degrees?
33.5º
37.3º
10.4º
29.6º
omit
Question 6
Given the vectors:
a
= (11 meters, 40º) and
b
= (22 meters, 90º)
What is the magnitude, or length, of
R
_{5}
= 3
a
 4
b
66.2 meters
41.5 meters
121.0 meters
71.4 meters
omit
Question 7
What is the direction of
R
_{5}
in degrees?
20.7º
290.7º
339.3º
110.7º
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