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VECTORS

Section 6.1 & 6.2. VECTORS. “still” measurements. “moving” measurements. Force Velocity Acceleration. Temperature Distance Height Area Volume. Magnitude. The relative size of an object or the “amount of something”. Two-Dimensional Vectors. Magnitude : the length of the segment

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VECTORS

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  1. Section 6.1 & 6.2 VECTORS

  2. “still” measurements “moving” measurements Force Velocity Acceleration • Temperature • Distance • Height • Area • Volume

  3. Magnitude • The relative size of an object or the “amount of something”

  4. Two-Dimensional Vectors • Magnitude: the length of the segment • Direction: the direction in which the arrow is pointing. Vector with components a & b

  5. Magnitude

  6. Ex) Draw

  7. Vector Notation (a,b) (0,0) *Called a linear combination S(x,y) R(x,y)

  8. Equivalent Vectors • Vectors that are the same length and the same direction are equivalent

  9. #1 Show vectors are equal • R=(-4,7) S=(-1,5), O=(0,0) P=(3,-2).

  10. “Component Form” (from origin): HEAD – TAIL

  11. Finding the Magnitude

  12. 2.)For the following examples let P=(-2,2) , Q=(3,4), R=(-2,5), and S=(2,-8). Find the component form and magnitude of the vectors below. a.) 2.)For the following examples let P=(-2,2) , Q=(3,4), R=(-2,5), and S=(2,-8). Find the component form and magnitude of the vectors below. Problem #2 b.) P=(-2,2) , Q=(3,4), R=(-2,5), and S=(2,-8)

  13. Adding Vectors

  14. Graph Head to Tail Graph Parallelogram v u u+v u u+v v

  15. Scalar Multiplication

  16. #3

  17. Dot Product • A way of “multiplying” vectors • Answer is a real number

  18. #4

  19. Orthognal • Orthogonal Vectors: vectors that are perpendicular (90°) to each other • Dot product will equal ZERO

  20. #5

  21. Direction Angles |v|

  22. #6 Find the horizontal and vertical components of vector v with direction angle 25° and magnitude 18.

  23. #7 Find the direction angle of the vector (*hint: find magnitude first)

  24. Applications • Velocity (speed & direction) • Speed = magnitude • Gravity (force & direction) • Force = magnitude

  25. 8. Hector is trying to get his dog to keep walking. He pulls on the leash with a force of 67 newtons, at an angle of 30 degrees above the horizontal. Determine the vertical and horizontal components

  26. 9. Helen is parasailing. She sits in a seat harness which is attached by a tow rope to a speedboat. The rope makes an angle of 51° with the horizontal and has a tension of 350 N. Determine the horizontal and vertical components of the tension force.

  27. 10. A plane is flying on a bearing of 65° at 500 mph. Find the component form of the velocity of the airplane *Bearing is the angle formed with due north measure clockwise

  28. 11. A basketball is shot at a 70° angle with thehorizontal direction. Its initial speed is 10 m/sec. Find the vertical and horizontal components of the vector.

  29. Vector Equations of Lines Equation of a line passing through v

  30. #12 a. (-2, 5) and (4, 2) b. (3, 4) and (6, -3)

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