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Introduction to Vectors

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Vectors ScalarsVectors Distance Time Mass Work Energy Speed Displacement Velocity Acceleration Force Momentum Torque Magnitude Only Magnitude and Direction

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Vectors have magnitude and direction, but no place Vectors

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Two vectors are equal if they have the same magnitude and the same direction

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Vectors Scaling Vectors

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Vectors Scaling a Displacement Vector

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Vectors Scaling a Change in Velocity Vector

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Vectors Vector Addition (Graphical)

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Vectors Vector Subtraction (Graphical)

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Vectors Vector Subtraction (Graphical)

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Vectors Vector Subtraction (Graphical)

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The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors that make a right angle to each other.

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x y The parallelogram method of vector resolution involves using an accurately drawn, scaled vector diagram to determine the components of the vector.

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x y The trigonometric method of vector resolution involves using trigonometric functions to determine the components of the vector.

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Vectors x y Vector Components

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A B R AxAx BxBx RxRx AyAy ByBy RyRy x y Adding Vectors using Vector Components

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A B R AxAx BxBx RxRx AyAy ByBy RyRy x y

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Vectors F2F2 22 F3F3 33 F4F4 44 F1F1 11

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F1F1 F2F2 F3F3 F4F4 11 22 33 44 F 1 = 50 N 1 = 30 o F 2 = 100 N 2 = 135 o F 3 = 30 N 3 = 250 o F 4 = 40 N 4 = 300 o 43.325.0 70.7 70.7 10.3 28.2 20.0 34.6 17.7 32.9 Adding Vectors using Vector Components

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Vectors F R = 37.4 N RR 17.7 32.9

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Vectors F1F1 F2F2 F3F3 F4F4 11 22 33 44 F 1 = 90 N 1 = 45 o F 2 = 80 N 2 = 150 o F 3 =50 N 3 = 220 o F 4 = 70 N 4 = 340 o 63.6 69.3 38.3 65.8 63.6 40.0 23.9 21.8 47.6 F R = 52.4 N RR 47.6 21.8

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