Practice Problems
Vector Addition
Topics:
On this worksheet you will practice adding vectors. Remember that when vectors are added graphically by using the
headtotail method
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.
Page Directions
The numerical values in this worksheet are randomly generated allowing students the opportunity to conveniently practice, and drill, common situations.
Before beginning any given worksheet, please look over all of the questions and make sure that there are
no duplicate
answers shown for the same question. If duplicates are present simply refresh the page until every answer is unique.
In order to check an answer
(even when you are just starting the worksheet on Question 1)
it is necessary to
any questions that you have not answered. Once you start submitting answers, the page may be checked as many times as necesasary without changing the randomized answers. Relevant scoring will be provided at the top of the page only when you answer all of the questions on your original submission.
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
= (19 meters, 0º) and
z
= (4 meters, 0º).
What is the magnitude, or length, of
R
_{1}
=
x
+ 2
z
?
42 meters
46 meters
11 meters
27 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.
7 meters
45 meters
61 meters
53 meters
omit
Question 3
What is the direction of
R
_{3}
if
R
_{3}
=
 R
_{2}
270º
0º
225º
180º
omit
Question 4
Given the vectors:
x
= (19 meters, 0º) and
a
= (5 meters, 45º)
What is the magnitude, or length, of
R
_{4}
=
x
+ 3
a
?
31.4 meters
34.0 meters
62.0 meters
31.4 meters
omit
Question 5
What is the direction of
R
_{4}
in degrees?
19.7º
19.7º
19.7º
25.3º
omit
Question 6
Given the vectors:
a
= (5 meters, 45º) and
b
= (28 meters, 90º)
What is the magnitude, or length, of
R
_{5}
= 3
a
 2
b
46.6 meters
71.0 meters
34.8 meters
46.6 meters
omit
Question 7
What is the direction of
R
_{5}
in degrees?
103.2º
13.2º
346.8º
283.2º
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