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Vectors

Vectors. On to Vectory !. A. B. Properties of Vectors. A = B Two vectors are considered equal if they have the same magnitude (size) and direction. A= B. Properties of Vectors. A + B = R

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Vectors

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  1. Vectors On to Vectory!

  2. A B Properties of Vectors • A = B • Two vectors are considered equal if they have the same magnitude (size) and direction. A=B

  3. Properties of Vectors • A + B = R • Regardless of how two vectors are added the resultant vector will remain the same. (Commutative Property of Equality) or B + A = R B A R

  4. C R B+ C B A VectorsIf three or more vectors are added, their sum is independent of the way in which they are grouped (Associative Property of Addition) A+B

  5. D C R B A VectorsIf three or more vectors are added, their sum is independent of the order in which they are added. (Commutative Property of Equality)

  6. A -A Negative Vectors

  7. B -B A R Subtraction of Vectors • A - B = R • Two vectors are considered equal if they have the same magnitude (size) and direction.

  8. 6A -6A Multiplicationof a vector by a scalar A Multiplying by a scalar quantity can change the magnitude of the vector. Or its direction.

  9. ̂ k ̂ i ̂ j Unit Vectors z x y

  10. Addition of Vectorsin the Same Directions

  11. 1 i 1 i 1 i 1 i 1 i 1 i = 2 i = 4 i = 6 i Addition of Vectorsin the Same Directions

  12. y R Ry Θ x Rx R = Rx+ Ry Or R = Rxi+ Ry j ^ ^ Vector Components

  13. Θ Trigonometric Functions • Sine sin Θ = opp/hyp or y/r • Thus y = r sin Θ • Cosine cos Θ = adj/hyp or x/r • Thus x = r cos Θ • Tangent • tan Θ = opp/adj or y/x • tan Θ is the slope of the line containing the resultant vector • Thus Θ = tan-1(y/x) y r or hypotenuse y or opposite side x x or adjacent side

  14. Ry =5 m sin(38.6°) =3 m R= 5 m Θ= 36.8° Rx =5 m cos(38.6°) =4 m R = 4 m i+ 3 mj Vector Components y x

  15. Component Addition y x Multiple Vectors can be added in this manner.

  16. A word about Trigonometryand the Unit Circle II I (-,+) (+,+) You need to pick a reference quadrant and axis. (-,-) (+,-) III IV

  17. The End …maybe. Go practice!

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