**Vector Proof**

Starter

Main Activity

Plenary

**L.O. Prove geometrical properties with vectors.**

Find the vector from K to L.

Find the vector from K to J.

Do you notice anything?

Starter

Find the vector from K to L.

2

a

+ 3

b

Find the vector from K to J.

4

a

+ 6

b

Do you notice anything?

One is double the other

What have we proved?

KL =

2

a

+ 3

b

KJ =

4

a

+ 6

b

One is double

the other.

What have we proved?

KL =

2

a

+ 3

b

KJ =

4

a

+ 6

b

One is double

the other.

They lie on a straight line

KL = LJ

Complete the Vector Proof sheet.

Main Activity Answers

(a) Yes (b) Yes (c) No (d) No (e) Yes (f) No

(a) 5:3 (b) 1:2 (c) 2:1 (d) 1:1 (e) 2:1 (f) 1:3

3:2

(a) p + q (b) p - q (c) 2q

(d) The lines are parallel (and AD is 1.5 x bigger than

MN)

Plenary

1

2

1

2

1

2

1

2

**Key**

Examples

Examples

**Activities**

**Activity**

Answers

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Worked

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