# Introduction to Vectors. Vectors ScalarsVectors Distance Time Mass Work Energy Speed Displacement Velocity Acceleration Force Momentum Torque Magnitude.

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Introduction to Vectors

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

Vectors have magnitude and direction, but no place Vectors

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

Vectors Scaling Vectors

Vectors Scaling a Displacement Vector

Vectors Scaling a Change in Velocity Vector

Vectors Vector Addition (Graphical)

Vectors Vector Subtraction (Graphical)

Vectors Vector Subtraction (Graphical)

Vectors Vector Subtraction (Graphical)

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.

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

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

Vectors x y Vector Components

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

A B R AxAx BxBx RxRx AyAy ByBy RyRy x y

Vectors F2F2 22 F3F3 33 F4F4 44 F1F1 11

F1F1 F2F2 F3F3 F4F4 11 22 33 44 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

Vectors F R = 37.4 N RR   17.7 32.9

Vectors F1F1 F2F2 F3F3 F4F4 11 22 33 44 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 RR 47.6 21.8

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