The Vector Unit Test
(not the unit vector test)
Fall 2015
MI-4
Name: ________________________
You may use your TI-89 calculator, but you must show all set-up for credit.
1. (3 pts) Dr. Torres is going to Springfield. He is travelling from IMSA at 63 mph in the
direction S 23 W . Will he go through Bloomington given that the location of Bloomington (from
IMSA) is given by the vector 50, 74 , where measurement are in miles? Explain clearly with
a picture.
2. Given vectors x  a, 2, a and y  2a, a  7, 6 .
a) (3 pts.) Find all values of a that make these vectors orthogonal to each other.
b) (3 pts.) Find all values of a that make these vectors parallel to each other.
MI4
Vector Exam 1
Fall 2015
3. Consider the vectors p = 4,1 and q =
1,1
a) (2 pts) Draw and label p, q, and projqp
b) (1 pt) Compute pq.
c) (2 pts) Compute projqp.
d) (1 pt) Compute p̂ .
e) (2 pts.) Compute |2p – 3q|
f) (1 pt) Find a vector of length 8 in the
opposite direction of p.
MI4
Vector Exam 2
Fall 2015
4. (8 pts) Given that BC is parallel to AD ,
1
2
BC  2 AD w  AB , u  AD , and F is the
2
3
midpoint of BC , find each of the following
vectors in terms of u and w .
a.
F
B
C
w
A
D
u
BC
b. AC
c. FD
d. CD
5. (5 pts) Two wires hold up the door to Dr. Condie’s
office, as shown at right. The angles that the wires make
with the ceiling are 30 and 55 , and the tension in the
wire with the 55 angle is |T2| = 200N. Find the tension
|T1| in the other wire and the mass of the door? Reminder:
the magnitude of g is 9.8 m/s2.
MI4
Vector Exam 3
T1
T2
door
Fall 2015
6a) (2 pts.) In the shown grid at right. sketch
v = 3, –2, 4.
z
b) (3 pts.) Find the angle between
v = 3, –2, 4 and w = 0, 2, –3 to the nearest
tenth of a degree.
y
x
7. (2 pts.) Given the two vectors a and b below, sketch a  2b .
a
b
8.(3 pts. ) If the vector v  3, 2 is rotated about the origin 50 in the clock-wise direction, find
the resulting vector.
MI4
Vector Exam 4
Fall 2015