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Unit 38Vectors

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

(i)

b - c

- c

b

(iii)

(ii)

c a

b

a

c

a b

(iv)

a

a c - b

a c

- 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) ,

where N is the midpoint of BD, (f)

?

?

?

?

?

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

- Express in terms of x and y,
- (i) (ii) (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 (a)

?

from part (b)

?

Hence A, P and E are collinear

?

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