Mathematical Investigations IV
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
and w  3,5 . Find:
a) Find v̂ , the unit vector in the direction of v .
b) Find the measure of the angle between v and w
c) Find projv w .
2) For what values of a will the angle formed by 3,5 and a,6 be obtuse?
3) For what values of a will the vectors 2a, a  4 and 1,a be orthogonal?
Mathematical Investigations IV
2013
Vector Unit Test
Name:_____________________
Mods __________
3) Given a  3,  4, 2 and b  2,5,0 ,
a) Sketch a .
z
y
b) Find 2a  3b
x
4) Let v and w be as drawn. Sketch the following vectors, clearly labeling your work.
a) v  2w
w
v
 
b) proj v w
w
v
Mathematical Investigations IV
2013
Vector Unit Test
Name:_____________________
Mods __________
5) The object shown in the figure is hanging in equilibrium, with |T1| = 20 Newtons and
|T2| = 25 Newtons.
We know T1  T2  0, mg  0,0 .
 20cos(30 )  25cos( )  0
Hence, 
20sin(30 )  25sin( )  9.8m
|T1| = 20 N
30
|T2| = 25 N

-mgj
(g = 9.8 m/s2)
Determine the measure of angle  and the mass, m, of the object. Round your answers to the
nearest tenth. Using the trusty TI 89 to solve gives   46.2 and m  2.9 kg
4 pts
6) Find the scalars (a, b) such that w  au  bv if w  15,32 , u  2, 1 , and v  3,5 .
w  au  bv  15,32  a 2, 1  b 3,5
2a  3b  15

 a  5b  32
 a  3 and b  7
Mathematical Investigations IV
2013
Vector Unit Test
Name:_____________________
Mods __________
7) Given a regular hexagon ABCDEF with center O, u  AG 
1
AF and v  AB (see figure
2
below), find each of the vectors in terms of u and v .
2 pts
a. CD  2u
2 pts
2 pts
b. AO  v  2u
2 pts
c. AE  v  4u
d.
E
CA  CO  OA
 v  AO
 v   v  2u 
 2v  2u
D
O
F
C
G
u
v
B
A