Mathematical Investigations IV
Fall 2013
Vector Unit Test
Name:_____________________
Mods __________
You may use a calculator on this exam, but must show all set-up. I should be able to recreate
your answer from your work.
1) If v  2,6
3 pts
a. Find the measure of the angle between v and w to the nearest tenth of a degree.
3 pts
b. Find 2w  v
3 pts
3 pts
and w  3, 1 . Find:
c. Find proj v w .
2) For what values of a will the vectors 2a, a  1 and a  1,  3 be orthogonal?
Mathematical Investigations IV
Fall 2013
Vector Unit Test
Name:_____________________
Mods __________
3) Given a  3, 2, 3 and b  6,  a 2 , a  a 2 ,
2 pts
a. Sketch a .
2 pts
b. Find â .
3 pts
c. Find all values of a so that a
z
y
is parallel to b .
x
4) Let v and w be as drawn. Sketch the following vectors, clearly labeling your work.
2 pts
a. v  2w
v
w
2 pts
 
b. proj v w
w
v
Mathematical Investigations IV
Fall 2013
6 pts
Vector Unit Test
Name:_____________________
Mods __________
5) The object shown in the figure is hanging in equilibrium. If the mass of the hanging weight is
12 kg, find the tensions in each wire; that is, find |T1| and |T2| . Round your answers to the
nearest tenth of a Newton.
T1
T2
40
65
-mgj
(g = 9.8 m/s2)
.
5 pts
6) Classify each of the following as a scalar (S), a vector (V), or meaningless (M).
a. 5u
b. u v
c.  u v  w
d.  u v  w
e. u vˆ
Mathematical Investigations IV
Fall 2013
6 pts
Vector Unit Test
Name:_____________________
Mods __________
7) A boat heads in the direction N 35 W at a speed of 20 knots. The tide runs at 6 knots in the
direction S 30 W . Find the resultant speed and direction of the boat.
Let t represent the tide h represent the heading, and R represent the resultant velocity of the boat.
By law of cosines, the length of R  h  t is given by
h t
6
65
 202  62  2  20  6  cos(65 ) 
u  v  18.29
h
t
Then, by law of sines
20
is
2
sin(65 ) sin( )

   17.3 , so the direction of R  h  t
18.29
6
R

35
N 52.3 W