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Form 5 Mathematics

Form 5 Mathematics. Displacement & Position vectors. Meet Amy, Betty & Cindy. Amy. Betty. Cindy. Amy lives at (2,1). Cindy lives at (-3,2). Betty lives at (4,6). What is the vector to get from Amy to Betty?. (. ). 2 5. B.

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Form 5 Mathematics

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  1. Form 5 Mathematics Displacement & Position vectors

  2. Meet Amy, Betty & Cindy Amy Betty Cindy

  3. Amy lives at (2,1) Cindy lives at (-3,2) Betty lives at (4,6) What is the vector to get from Amy to Betty? ( ) 2 5 B When Amy gets to Betty’s house they then wants to go to Cindy’s house. What is the vector from Betty to Cindy? Amy C A ( -7 -4 ) Betty What vector represents Amy travelling to Cindy’s house? ( -5 1 ) Cindy

  4. Recap of Amy’s travels ( ) 2 5 AB= ( ) -7 -4 BC= B ( ) -5 1 AC= C A 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.

  5. Meet Luke, Matthew & Nicholas Luke Matthew Nicholas

  6. Luke, Matthew and Nicholas • Luke lives at (3,-2) • Matthew lives at (-5,-2) • Nicholas lives at (3,4) Plot L, M & N. Luke Matthew Nicholas

  7. Luke, Matthew and Nicholas N Luke Matthew M L Nicholas

  8. Luke, Matthew and Nicholas ( ) -8 0 What is the vector LM? LM= ( ) 8 6 What is the vector MN? MN= Luke ( ) 0 6 What is the resultant vector LN? LN= Matthew Draw these vectors on your graph. (Remember to use two arrows on your resultant vector.) Nicholas

  9. Position Vectors A position vector is a vector whose initial point is the origin. Where is the origin?

  10. For example… This is the position vector OD. D O

  11. Amy, Betty & Cindy Suppose Amy, Betty and Cindy could only get to each others houses by going to the bus station. B Amy C A O Betty Cindy

  12. Cindy Betty Amy AB=AO + OB What is the relationship between AO and OA? B Do you notice a relationship between the coordinates of A and the position vector OA? C A O AB is made up of two position vectors. OA and OB. Split AC into two position vectors.

  13. 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.

  14. 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

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