1.

 a f b g c h d i e j 2. Magnitude of a = 5
Magnitude of = 6.40
Magnitude of c = 3.61
Magnitude of = 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 + 3and = 3i − 2j .
BA = a - b = 2i + 3j − (3i − 2j) = -i + 5j

c. = 2(2i + 3j) − 3(3i - 2j ) = -5i + 12j

d. Midpoint of OC = 1/2( -5i + 12) = -2.5+ 6
Coordinates of D are (-2.5, 6)