Vector Quiz #1
Name:_________________________
Calculator Allowed. You must show enough work to enable me to recreate your results.
1.
Find all value(s) of a such that  a, 2a is a unit vector.
We want
2.
a 2   2a   1  5a 2  1  a  
2
1
5

5
5
A pilot sets her plane to fly on “autopilot” in the direction N30W at a speed of 400 mph.
A few minutes later, she checks the instruments and discovers that, due to the wind, the
plane has actually been flying in the direction N10W at 430 mph. What is the speed and
direction of the wind? Support your results with a picture.
IMSA
Vectors - 1
F12
3.
In triangle ABC, Y is the midpoint of AB ,
1
AX  AC , and Z is the midpoint of BX .
3
Find the following vectors in terms of
v  AX and w  AY .
B
Y
Z
w
A

a.
AC  3v
c.
CX  2v

C
X
v
  
b. BC  BA AC  2w  3v

d. XZ :

 
 1   
AX  2 XZ  AB  XZ   AB  AX 
2

1
  2w  v 
2
1
 w v
2
4. Given the vectors v  4, 4 and w  1,2 , find the following:
a. v  16  16  4 2
b. v  2w   2,0   2
c.
vˆ 
1
1
v
4, 4 
v
4 2
1
1
,
2
2
d. Sketch w and find the angle between w and the positive x-axis.
d. Find the vector of length 3 units in the direction of v .
3
3
,
This would be 3vˆ 
2
2
IMSA
Vectors - 2
F12