If a = 
, b = 
, c = 
, d = 
and e =
1. Find the following and leave the answer in matrix form:
|
a |
a + b |
|
b
|
b − c |
|
c
|
5c |
|
d
|
-3e |
|
e
|
e + 2c |
|
f
|
2a + 3c |
|
g
|
d − 4e |
|
h
|
3b − 2e |
|
i
|
a + b + c |
|
j
|
2(a + b − e) |
2. Find the length or magnitude of a, b, c, d and e. Give answers to 3 significant figures where appropriate.
3. Illustrate on a diagram, the following vector additions and subtractions. Draw the resultant vector and label it r.
|
a |
a + c |
|
b
|
b + c |
|
c
|
a + b + c |
|
d
|
a − b |
|
e
|
b − e |
|
f
|
3c + 4d |
|
g
|
2d − 3e |
|
h
|
4b − d |
|
i
|
a + b − c |
|
j
|
a + b + c + d + e |
4. Express a, b, c, d, and e as unit vectors.
5. Calculate the following using unit vector notation. A diagram is not needed. Check your answers with those calculated in question 1.
|
a |
a + b |
|
b
|
b − c |
|
c
|
5c |
|
d
|
-3e |
|
e
|
e + 2c |
|
f
|
2a + 3c |
|
g
|
d − 4e |
|
h
|
3b − 2e |
|
i
|
a + b + c |
|
j
|
2(a + b − e) |
6. Find the number p such that p+ = 
7. Find numbers s and t such that 
8. a. If p = 6i -2j, q = 3j -2i and r = 13j − 4i, show that there is a number s such that p + sq = r.
9. The points C and D have coordinates (4, 2) and (2, 3). Find the coordinates of the points E, F, G, H, I and J given by the following vector equations.
|
a |
e = 4c |
|
b
|
f = -2d |
|
c
|
g = c − d |
|
d
|
h = d - 3c |
|
e
|
i = d + 3c |
|
f
|
j = 1/2(d + 3c) |
10. A is the point (2, 3) and B is the point (3, -2)
a. What are the position vectors of A and B as column vectors?
b. Write a and b as unit vectors and find BA.
c. If c = 2a − 3b, find the coordinates of c. Show on a diagram.
d. If a point D is the midpoint of OC find its coordinates.
