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Vectors

A. O. a. a. ~. ~. Vectors. Some terms to know:. Vectors: Lines with length (magnitude) and direction. Vector. Zero vector. or Null vector. Magnitude of is represented by. a. | |. Or magnitude of is represented by. Direction is represented by column vector. a. ~.

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Vectors

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  1. A O a a ~ ~ Vectors Some terms to know: Vectors: Lines with length (magnitude) and direction Vector

  2. Zero vector or Null vector Magnitude of is represented by a | | Or magnitude of is represented by Direction is represented by column vector a ~ Vectors • No length • No direction

  3. Movement parallel to the x-axis Movement parallel to the y-axis Q P Vectors y= +4 x= +2

  4. Q P Vectors y= - 4 x= - 2

  5. Q S P R Vectors Equal vectors or equivalent vectors Same length Same direction

  6. Q S P R Vectors Negative vectors Same length opposite direction NOTE: Negative sign reverses the direction

  7. Let’s do up Exercise 5A in your foolscap paper Q. 1, 3, 5

  8. Vectors Vector addition Vector subtraction

  9. Q Q R R P P Vectors Triangle law of vector addition Ending point Starting point Parallelogram law of vector addition Ending point Starting point S

  10. Let’s do up Exercise 5B in your foolscap paper Q. 3, 4, 6, 7

  11. Vectors Scalar multiplication

  12. Let’s do up Exercise 5C in your foolscap paper Q. 1, 5, 10

  13. P Q Vectors y= - 5 x= 2

  14. Q S P R Vectors Parallel vectors Same gradient

  15. Q P Vectors Gradient of vector y= +4 x= +2

  16. R Q P P Vectors Collinear vectors Lie on the same straight line P, Q and R are collinear => P, Q and R lie on the same straight line

  17. Eg. Given c = , find (a) |2c| (b) |-2c| (c) 2|c| ~ (a) 2c = 2 Vectors |2c|=

  18. Eg. Given c = , find (a) |2c| (b) |-2c| (c) 2|c| ~ (b) -2c = -2 Vectors |-2c|=

  19. Eg. Given c = , find (a) |2c| (b) |-2c| (c) 2|c| ~ Vectors (c) 2|c|=

  20. Vectors Notice: |2c| = 10 units |-2c| = 10 units 2|c| = 10 units Therefore, |2c| = |-2c| = 2|c| In conclusion: |kc| = |-kc| = k|c|, where k is any positive number

  21. Vectors Eg. Given a = and b = , find (a) |a| + |b| (b) |a+b| ~ ~ |a| + |b| a+b |a+b|= Note: |a| + |b| ≠ |a + b|

  22. Vectors Eg. Given a = and b = , find (c) |2b-a| (d) 2|b| + |a| ~ ~ 2b-a 2|b| + |a| |2b-a|= Note: |2b -a| ≠ 2|b| - |a|

  23. Let’s do up Exercise 5D in your foolscap paper Q. 1, 6, 8

  24. y P O x Vectors Position vectors: always with respect to origin Can you tell me what is the position vector of P?

  25. y P O x Vectors In general, position vector of any point, say P, is given by

  26. Q Vectors Position vectors y P O x

  27. Let’s do up Exercise 5E in your foolscap paper Q. 3, 6, 12

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