Form 5 Mathematics

•Displacement & Position vectors

Meet Amy, Betty & Cindy

Amy

Betty

Cindy

Amy lives at (2,1)

Amy

Betty

Cindy

A

Betty lives at (4,6)

B

Cindy lives at (-3,2)

C

What is the vector to get from Amy to Betty?

25( )

When Amy gets to Betty’s house they then wants to go to Cindy’s house.What is the vector from Betty to Cindy? ( )-7

-4

What vector represents Amy travelling to Cindy’s house?

( )-51

Recap of Amy’s travels

A

B

C

AB= ( 25)

BC= (-7-4)

AC= (-51)

Do you notice a relationship between the first two vectors above and AC?

AC is the resultant vector of AB and BC. We represent this by putting a second arrow on the vector.

Meet Luke, Matthew & Nicholas

Luke

Matthew

Nicholas

Luke, Matthew and Nicholas

Luke

Matthew

Nicholas

• Luke lives at (3,-2)

• Matthew lives at (-5,-2)

• Nicholas lives at (3,4)

Plot L, M & N.

Luke, Matthew and Nicholas

LM

NLuke

Matthew

Nicholas

Luke, Matthew and Nicholas

Luke

Matthew

Nicholas

What is the vector LM? LM= (-8 0 )

What is the vector MN? MN=( 86)

What is the resultant vector LN? LN= ( 06)

Draw these vectors on your graph. (Remember to use two arrows on your resultant vector.)

Position Vectors

A position vector is a vector whose initial point is the origin.

Where is the origin?

For example…

O

D

This is the position vector OD.

Amy, Betty & Cindy

Amy

Betty

Cindy

A

B

C

Suppose Amy, Betty and Cindy could only get to each others houses by going to the bus station.

O

Amy

BettyCindy

A

B

C

O

AB=AO + OB

AB is made up of two position vectors.OA and OB.

What is the relationship between AO and OA?

Split AC into two position vectors.

Do you notice a relationship between the coordinates of A and the position vector OA?

Let us try this question!

If is A(2,3), B(5,4) and C(-1,3),

Calculate OA, OB and OC.

Calculate AB.

Calculate BC.

Calculate AC.

Try this question!

K(-2,1), L(1,4), M(1,1)

Convert the above coordinates to position vectors.

Use these position vectors to calculate LM and KM