# Quiz #1 Section 2

```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.
2.
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
c.
CX
v
C
X

b. BC


d. XZ
4. Given the vectors v  4, 4 and w  1,2 , find the following:
a. v
b. v  2w
c. v̂
d. Sketch w and find the angle between w and the positive x-axis.
a.
IMSA
Find the vector of length 3 units in the direction of v .
Vectors - 2
F12
```