1. Unit 38 Vectors Presentation 1Equal Vectors Presentation 2Components Presentation 3Vector Expressions Presentation 4Addition and Subtraction of Vectors Presentation 5Vector Geometry 1 Presentation 6Vector Geometry 2

2. Unit 38 38.1 Equal Vectors

3. In the following diagram, state Which pairs of vectors are equivalent and which pairs of vectors are opposite directions Equivalent vectors: a and b b and i f and g Vectors in opposite directions c and b e and j ? ? ? ? ?

4. Unit 38 38.2 Components

5. Does ? ? ? ? ? Given that,, calculate ? ? ? ? ? ? No

6. Unit 38 38.3 Vector Expressions

7. Write down each of the following in terms of d and/or e. (a) (b) (c) ? ? ? ? ? Mark clearly on the diagram (a) the point P such that (b) the point Q such that Q P ?

8. Unit 38 38.4 Addition and Subtraction of Vectors

9. Given that On the grid below, illustrate the following vectors (i)b – c (ii) c + a (iii)a + b (iv)a + c – b b - c - c b (i) (ii) c + a c a (iii) a + b b a (iv) a + c - b a + c - b

10. Unit 38 38.5 Vector Geometry 1

11. Express, in terms of u and v, (a) (b) (c), where M is the midpoint of AC, ? ? ?

12. Express, in terms of u and v, (d) (e), where N is the midpoint of BD, (f) ? ? ? ? ?

13. What can you deduce about points M and N? They are coincident. Hence and

14. Unit 38 38.6 Vector Geometry 2

15. (a)Express in terms of x and y, (i)(ii)(iii) Solution In the figure above, ABCD is a parallelogram such that and. The point P is on DB such that (i) (ii) (iii) ? ? ? ?

16. ? In the figure above, ABCD is a parallelogram such that and. The point P is on DB such that (b) Show that Solution ?

17. In the figure above, ABCD is a parallelogram such that and. The point P is on DB such that (c) Given that E is the midpoint of DC, prove that A, P and E are collinear. Solution so Hence A, P and E are collinear ? ? ? ? ? from part (b) from part (a)