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Vector Mathematics AP

# Vector Mathematics AP - Vector Mathematics Adding...

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Vector Mathematics Adding, Subtracting, Multiplying and Dividing

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Why? One can add 23 kg and 42 kg and get 65 kg. However, one cannot add together 23 m/s south and 42 m/s southeast and get 65 m/ s south-southeast. Vectors addition takes into account adding both magnitude and direction
Words Vector : A measured quantity with both magnitude (the how big part) and direction Scalar : A measured quantity with magnitude only Resultant Vector : The final vector of a vector math problem

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“Math” Coordinate System (Direction) 90º 180º 270º
Polar Coordinate System (Direction and Magnitude)

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Polar  “Math” (Cartesian) 2 2 1 cos sin tan r x y x r y r y x θ θ θ - = + = = = x y r θ

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Vector addition Two Ways: 1. Graphically: Draw vectors to scale, Tip to Tail, and the resultant is the straight line from start to finish 2. Mathematically: Employ vector math analysis to solve for the resultant vector
Graphically 2-D Right A = 5.0 m @ 0° B = 5.0 m @ 90° Solve A + B R Start R=7.1 m @ 45°

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Important You can add vectors in any order and yield the same resultant.

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