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

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Presentation transcript:

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

Unit 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 Components

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

Unit Vector Expressions

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 ?

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

Unit 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), where N is the midpoint of BD, (f) ? ? ? ? ?

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

Unit Vector Geometry 2

(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) ? ? ? ?

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