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? 2525 () When Amy gets to Betty’s house they then wants to go to Cindy’s house. What is the vector from Betty to Cindy? () What vector represents Amy travelling to Cindy’s house? () -5 1

Recap of Amy’s travels A B C AB= ( 2525 ) BC= ( ) AC= ( -5 1 ) 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 N Luke Matthew Nicholas

Luke, Matthew and Nicholas Luke Matthew Nicholas What is the vector LM?LM= ( -8 0 ) What is the vector MN?MN= ( 8686 ) What is the resultant vector LN?LN= ( 0606 ) 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 Betty Cindy 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