Unit 38 Vectors Presentation 1 Equal Vectors Presentation

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

Unit 38 38. 1 Equal Vectors

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

Unit 38 38. 2 Components

Given that , , calculate ? ? ? ? Does ? No

Unit 38 38. 3 Vector Expressions

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

Unit 38 38. 4 Addition and Subtraction of Vectors

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 (iii) (ii) b a+b a c (iv) a + c - b a+c c+a a -b

Unit 38 38. 5 Vector Geometry 1

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

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

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

Unit 38 38. 6 Vector Geometry 2

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

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

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 ? ? ? from part (b) ? Hence A, P and E are collinear from part (a)