Vectors Worksheet in Geometry
1. Graphic Interpretation of Vectors.
a. Write a vector equation to represent
the vector drawn on the graph to
the right. Label it w.
b. Graph the following two vectors.
v= 3
–4
u= 9
6
t+
t +
3
12
–3
3


c. Describe w in terms of u and v.
2. Phoebe Jane is driving out across the desert (where she can’t hurt anyone) on a
bearing of ( N 77.3196° E ) at a velocity of 82 miles per hour.
a. _____________________
Express her velocity as a vector in polar form.
b. _____________________
Express her velocity as a vector in Cartesian
component form.
3. Find the magnitude and bearing of a vector

21
–28
.
a. _____________________
Magnitude
b. _____________________
Bearing (be careful!)
4. A force vector of magnitude 65 N is pulling on a sled at an angle of 14.25°. Resolve
the vector into its horizontal and vertical components. Show working.
a. _____________________
Horizontal component
b. _____________________
Vertical component
5. ______________________ Ben Franklin’s kite had 58 meters of string out when its
horizontal distance from Ben was 40 meters. Assuming that the string was taut in
the wind, how high was his kite? (3 pts.)
6. Calculate the dot product for each pair of vectors below.
a.
___________________

3
–5
 and  74 
b.
___________________

–3
4
 and 
c.
___________________
 23  and 
12
9
4
–5


7. Calculate the angle between the same three pairs of vectors to the nearest tenth of a
degree.
a.
___________________

3
–5
b.
___________________

–3
4
c.
___________________

2
3
 and 
 and 
 and 
7
4
12
9
4
–5



8. Identify whether each of the following pairs of vectors are perpendicular, parallel, or
neither by circling the appropriate relationship.
a.
 42  and  84 
parallel
perpendicular
neither
b.
 27  and  84 
parallel
perpendicular
neither
c.

4
–3
 and 
–6
–8
parallel
perpendicular
neither
d.

12
6
 and 
14
7

parallel
perpendicular
neither
e.

 and  38 
parallel
perpendicular
neither
16
–6
