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 475 miles per hour in the direction N35W. The velocity vector of
the plane is given by 475 cos(125), 475 sin(125).
_____ If |v| = |w| and v̂ = ŵ then v = w.
a
_____ |v| = vv.
_____ In the diagram at right, a + b = c.
b
c
2) Given vectors x  a,2 and y  2a  1, 5 .
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 = 1, 4 and q = –2, 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 |2p – 3q|
f) (1 pt.) Find a vector of length 8 with the
same direction as p.
MI4
Vector Exam 2
Fall 2012
4) (5 pts.) A pilot desires to fly in the direction S55E at a speed of 450 knots. There is a wind
blowing at 30 knots in direction N20E. At what speed and directionshould 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 35 and 60, and the tension in the wire with
the 60 angle is |T2| = 400N. 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.
35
T1
60
T2
prop
–mgj
jj
MI4
Vector Exam 3
Fall 2012
6)a) (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) 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  3,2 is rotated about the origin 50 in the clock-wise direction, find
the resulting vector.
MI4
Vector Exam 4
Fall 2012