Mathematical Investigations IV Vector Unit Test Name: _____________________
Fall 2013 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:
2 pts a. Find ˆ , the unit vector in the direction of v .
3 pts b. Find the measure of the angle between v and w to the nearest tenth of a degree.
3 pts c. Find proj v w .
3 pts 2) For what values of a will the angle formed by 3,5 and a ,6 be obtuse?
3 pts 3) For what values of a will the vectors

2 ,

4 and 1, a be orthogonal?

Mathematical Investigations IV Vector Unit Test Name: _____________________
Fall 2013
4) Given a

3, 4, 2 and b
 
2,5,0 ,
Mods __________
2 pts a. Sketch a .
3 pts b. Find 2 a

3 b z x
4) Let v and w be as drawn. Sketch the following vectors, clearly labeling your work.
2 pts a. v

2 w v w
2 pts b. proj v
  w v y

6 pts
4 pts
Mathematical Investigations IV Vector Unit Test Name: _____________________
Fall 2013 Mods __________
5) The object shown in the figure is hanging in equilibrium, with | T
1
| = 20 Newtons and
| T
2
| = 25 Newtons.
| T
1
| = 20 N | T
2
| = 25 N
30
 
mgj ( g = 9.8 m/s
2
)
Determine the measure of angle
 and the mass, m , of the object. Round your answers to the nearest tenth.
6) Find the scalars ( , ) such that w
 au
 bv if w
 
15,32 , u
  v
 
3,5 .

Mathematical Investigations IV Vector Unit Test Name: _____________________
Fall 2013 Mods __________
7) Given a regular hexagon ABCDEF with center O, u

AG

1
2
AF and v

AB (see figure below), find each of the vectors in terms of u and v .
2 pts a. CD
 2 pts b. AO

2 pts c. AE

2 pts d. CA

E D
F
G u
A
O v
B
C