Number 
Question 
Answer 
See the work 
1.

If a = <6,0,3> and b = <4,2,3>, find a • b =________.

15 
The work
Point Cost: 1 
2.

If u = <5,5,1> and v= <6,2,8>
Compute ______
Compute ______
Compute u•v =______

Compute 7.14143 Compute
10.19804
Compute u•v = 28 
The work
Point Cost: 1 
3.

Find a • b if
= 7,
= 4, and the angle between a and b is π/10 radians. a•b=_________

a•b= 26.62958 
The work
Point Cost: 2 
4.

Find a•b if a= <2,5,3> and b= <1,5,5> Is the angle between the vectors ”acute”, ”obtuse” or ”right”?

12
Obtuse

The work
Point Cost: 2 
5.

Find a•b if a= <3,2,2> and b= <0,1,0> and Is the angle between the vectors ”acute”, ”obtuse” or ”right”?

2
Obtuse

The work
Point Cost: 2 
6.

Find a vector orthogonal to both
< 5, 3, 0 > and to < 0, 3, 3 > of the form
< 1, ____, _____ >

< 1, 5/3, 5/3 >

The work
Point Cost: 3 
7.

Assume that , , and
.
What is the value of ?

2240

The work
Point Cost: 4 
8.

Compute the dot product .

19

The work
Point Cost: 1 
9.

The force on an object is .
For the vector , find:
(a)
The component of parallel to :
(b)
The component of perpendicular to :
The work, W, done by force
through
displacement :

(a):
(b):
W = 68

The work
Point Cost: 3 
10.

For what values of b are the vectors and
orthogonal?
b =

b = 0, 4 4

The work
Point Cost: 3 
11.

Perform the following operations on the vectors
, , and .

10
< 18,9,18 >
117
2

The work
Point Cost: 3 
12.

Determine if the pairs of vectors below are ”parallel”, ”orthogonal”, or ”neither”.
a= <5,2,1> and b= <15,6,87> are a= <5,2,1> and
b= <15,6,3> are a= <5,2,1> and b= <15,6,2> are

Orthogonal Parallel Neither

The work
Point Cost: 2 
13.

What is the angle in radians between the vectors
a= <9,5,6> and b= <7,7,2>?

1.2319859

The work
Point Cost: 2 
14.

A rectangular box has length 19 inches, width 7 inches, and a height of 11 inches. Find the angle between the diagonal of the base and the diagonal of the left hand side

Angle in radians: 1.3841131 Angle in degrees: 79.303984

The work
Point Cost: 5 
15.

Find the scalar and vector projection of the vector b=<4,5,1>
onto the vector a= <3,1,1>.

Scalar projection: 5.427204202 Vector projection: <54/11,18/11,18/11>

The work
Point Cost: 3 
16.

Find the scalar and vector projection of the vector b= <1,1,5>
onto the vector a= <1,3,1>.

Scalar projection: 2.110579412 Vector projection <7/11, 21/11, 7/11>

The work 
17.

Gandalf the Grey started in a Forest at a point with coordinates (1, 3). He arrives in these Hills at the point (0, 8). If he begins to walk in the direction of the vector v= 3i+1j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn.

(7/5, 3.8)

The work 
18.

A constant force F= 2i+3j+3k moves an object along a straight line from the point (0, 1, 4) to the point (0, 3,4). Find the work done if the distance is measured in meters and the force in newtons.

36 J

The work 
19.

A constant force F= 4i+2j+7k moves an object along a straight line from point (1, 7, 7) to point (10, 0, 3). Find the work done if the distance is measured in meters and the magnitude of the force is measured in newtons.

Work: 100 Nm

The work 
20.

A woman exerts a horizontal force of 9 pounds on a box as she pushes it up a ramp that is 7 feet long and inclined at an angle of 30 degrees above the horizontal. Find the work done on the box.

Work: 54.55960043 ftlb

The work 
