1.
a |
f
|
||
b
|
g
|
||
c
|
h
|
||
d
|
i
|
||
e
|
j
|
2. Magnitude of a = 5
Magnitude of b = 6.40
Magnitude of c = 3.61
Magnitude of d = 4
Magnitude of e = 5.39
3. Illustrate on a diagram, the following vector additions and subtractions. Draw the resultant vector and label it r.
a |
f
|
||
b
|
g | ||
c
|
h | ||
d
|
i | ||
e
|
j |
4. a = 3i + 4j
b = -4i + 5j
c = 3i − 2j
d = 4j
e = -2i − 5j
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 = 3i + 4j + (-4i + 5j) = -i + 9j |
b
|
-4i + 5j − ( 3i - 2j) = -7i + 7j |
c
|
5(3i - 2j) = 15i − 10j |
d
|
-3(-2i - 5j) = 6i + 15j |
e
|
-2i − 5j + 2(3i - 2j) = 4i − 9j |
f
|
2(3i + 4j) + 3(3i − 2j) = 15i +2j |
g
|
4j - 4(-2i - 5j) = 8i +24j |
h
|
3(-4i + 5j) - 2(-2i - 5j) = -8i + 25j |
i
|
3i + 4j + (-4i + 5j) + (3i − 2j) = 2i +7j |
j
|
2((3i + 4j) + (-4i + 5j) − (-2i - 5j)) = 2(i +14j) = 2i + 28j |
6. p = 2
7. s = -1 and t = -1
8. s = 5
9. The points C and D have coordinates (4, 2) and (2, 3). Plot the points E, F, G, H, I and J given by the following vector equations, and state their coordinates.
a |
(16, 8) |
b
|
(-4, -6) |
c
|
(2, -1) |
d
|
(-10, -3) |
e
|
(14, 9) |
f
|
(7, 4.5) |
10.
a. a = , b =
b. a = 2i + 3j and b = 3i − 2j .
BA = a - b = 2i + 3j − (3i − 2j) = -i + 5j
c. c = 2(2i + 3j) − 3(3i - 2j ) = -5i + 12j
d. Midpoint of OC = 1/2( -5i + 12j ) = -2.5i + 6j
Coordinates of D are (-2.5, 6)