MI 4
Vectors Quiz 1
Sheets 1-4
Name _________________
Calculator Allowed
Draw well labeled diagrams to explain your answers and show sufficient work
1
a. Given the vectors v  2,4 and w  1,3 . Draw and label vectors v and w and then
show how to get v  w geometrically. Draw and label v  w
b. Find the angle between v and w .
c. Find the following for the vectors in part (a):
v =
2v  3w =
v̂ =
2. For a parallelogram ABCD, suppose G is a midpoint of AB and E & F trisect AC. If AG = u
and AD = w . Find the following in terms of vectors u and w :
a. AC =
B
G
b. AF =
A
C
E
F
D
c. FD =
IMSA
Vectors Q1
F13
MI 4
Vectors Quiz 1
Sheets 1-4
Name _________________
3. A plane which can fly at 600 mph desires to travel in the direction N 40 W but he must
contend with a 45 mph wind from the east (that is, a wind blowing westward) . What direction
should the plane take to compensate for the wind? Find the speed of the plane after the effect of
the wind is taken into account. Draw a well labeled diagram to justify your answer. Round your
answer to the nearest hundredth
4. Given vectors x  3, a and y  5,2a  1 .
a. Find all values of a that make these vectors perpendicular to each other.
b. Find all values of a that make these vectors parallel to each other.
IMSA
Vectors Q1
F13