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Vectors

Vectors. 6001. INTRODUCTION SCALAR QUANTITIES: _______________________________________________________ VECTOR QUANTITIES: ________________________________________________________. Magnitude only. Magnitude and direction. x is negative add . Geometry: Line Segment Vector .

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Vectors

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  1. Vectors 6001

  2. INTRODUCTION SCALAR QUANTITIES: _______________________________________________________ VECTOR QUANTITIES: ________________________________________________________ Magnitude only Magnitude and direction x is negative add • Geometry: Line Segment Vector y only negative add length

  3. Vocabulary and Notation: Standard Position: Magnitude (____________) Amplitude /Direction Angle (____________) Bearing: Equal Vectors : Opposite Vectors: Zero Vector: Unit Vector: Initial point and terminal point (where arrow is) Initial point origin length Counter clockwise From the x-axis B Clockwise from the North B A Same direction, same magnitude A Same magnitude, opposite direction 0 magnitude called a point vector Length 1

  4. Component Form: chevrons Vertical = y Horizontal = x

  5. Component Form: Graphically count

  6. Component Form: Numerically Vector has endpoints A ( 4, -6) and B ( -6 , 1 ). Find the component form of Vector has component form and initial point A ( -3, -2) Find the terminal point . B(x,y)

  7. Protractor Skills: Examples: A Sketch the vector A with Magnitude : 50 mm Amplitude: θ = 20o Measure the magnitude and amplitude. Examples: B Sketch the vector B with Magnitude : 70 mm Bearing: θ = 135o Measure the magnitude and amplitude.

  8. A

  9. DOT Paper Sketch the vector C with Initial point ( 0 , 0 ) and Terminal point ( -3 , 5 ) Find the component form of the vector. Sketch the vector D with Initial point ( 0 , 0 ) and Terminal point ( 6 , -2 ) Find the component form of the vector.

  10. Examples: Sketch the vector E with Initial point ( 4 , 5 ) and Terminal point ( -1 , -3 ) Find the component form of the vector. Sketch the vector F with Initial point ( -2 , -3 ) and Terminal point ( 4 , 1 ) Find the component form of the vector.

  11. Standard Position: Find the component form of the vector. Draw the vector in standard position. count numerically

  12. TRIG Component Form: y x magnitude

  13. Trig component form Find the component from of a vector with Standard component trig standard

  14. Vectors 6002

  15. Magnitude and Amplitude: Magnitude is the length of the vector. Amplitude θ is the direction angle - Rem: positive direction Rem: if x is negative add 180o if y-only is negative add 360o

  16. Find the magnitude and amplitude of the vector:

  17. Unit Vector in the direction of : To find the unit vector in the direction of Divide the vector by its magnitude.

  18. Adding and Subtracting Vectors Protractor Skills: Adding: Heel to Toe b a+b a

  19. DOT Paper Adding: Heel to Toe b a

  20. Adding and Subtracting Vectors Protractor Skills: Subtracting: Toe to Toe - must point toward the subtracting vector a - b b - a b a

  21. DOT Paper Subtracting: Toe to Toe b a

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