The Vector Unit Test
(not the unit vector test)
Fall 2012
MI-4
Name: ________________________
You may use your TI-89 calculator, but you must show all set-up for credit.
1) (2 pts. each) True or false (no work necessary):
_____ A plane is traveling at 525 miles per hour in the direction N20W. The velocity vector of
the plane is given by   525 cos(20), 525 sin(20).
_____ If and v̂ = ŵ then v = w.
_____ v  v v
a
_____ In the diagram at right, a  b = c.
b
c
2) Given vectors x  a,2 and y  5,2a  1 .
a) (3 pts.) Find all values of a that make these vectors perpendicular to each other.
b) (3 pts.) Find all values of a that make these vectors parallel to each other.
MI4
Vector Exam 1
Fall 2012
3) Consider the vectors p = 2, 3 and q = –1, 2.
a) (2 pts.) Draw and label p and q.
b) (1 pt.) Compute pq.
c) (2 pts.) Compute projpq.
d) (1 pt.) Compute p̂ .
e) (2 pts.) Compute |3p – 2q|
f) (1 pt.) Find a vector of length 4 with the
same direction as p.
MI4
Vector Exam 2
Fall 2012
4) (5 pts.) A pilot desires to fly in the direction N55E at a speed of 450 knots. There is a wind
blowing at 30 knots in direction S20E. At what speed and direction should the pilot fly to
compensate for the wind?
5) (5 pts.) Two wires hold up a prop in a movie set, as
shown at right. The angles that the wires make with the
ceiling are 15 and 65, and the tension in the wire with
the 65 angle is |T2| = 200N. What is the tension |T1| in the
other wire? And what is the mass of the prop? Reminder:
the magnitude of g is 9.8 m/s2.
15
T1
65
T2
prop
–mgj
jj
MI4
Vector Exam 3
Fall 2012
6)a) (2 pts.) In the shown grid at right. sketch
v = 3, –2, 2.
z
b) (3 pts.) Find the angle between
v = 3, –2, 2 and w = 1, 3, –3 to the nearest
tenth of a degree.
y
x
7) a) (2 pts.) Givenr the two vectors a and b
below, sketch a  b .
b) (2 pts.) Given ther two vectors a and b
below, sketch projar b
a
a
b
b
8) (3 pts. ) If the vector v  1,2 is rotated about the origin 2 50 in the clock-wise direction, find
the resulting vector.
MI4
Vector Exam 4
Fall 2012