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Vectors4A

# Vectors4A - VECTORS Properties of Vectors DEF A vector is a...

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1 VECTORS DEF : A vector is a quantity that has both magnitude and direction. DEF : A scalar is a quantity that has magnitude but NO direction. Ex . Vectors Scalars Force Temperature Velocity Time Displacement Mass Momentum Speed Vector Notation A – Boldface letters A G - Arrow above letter A – Magnitude of vector A A vector is defined graphically by an arrow whose length is proportional to the magnitude of the vector quantity. The direction of the arrow points in the direction of the vector quantity. Adding Vectors Graphically Consider adding two vectors A and B graphically. The two vectors are shown below. q A B A B R f f 1. Select an appropriate scale. (Ex. 20 cm = 5 N) 2. Draw vector A to scale and in the proper direction. 3. Draw vector B to the same scale with its tail at the tip of A and in the proper direction. 4. The resultant vector R = A + B is the vector drawn from the tail of vector A to the tip of vector B . 5. Calculate the magnitude of the resultant vector R using the selected scale and measure its direction with a protractor. 6. This same process applies if you add more than two vectors. This method of adding vectors graphically is also referred to as the head-to-tail method, analytical method, and geometric method. Properties of Vectors 1 . A + B = B + A (commutative Law) 2. A + (B + C) = (A + B) + C (associative Law) 3. A + (-A) = 0 (Negative of a vector) 4. A B = A + (-B) (vector subtraction) 5. B = s A (vector multiplied by a scalar) A B A B B A A + B B + A (1) A B C B C (2) A - A = 0 (3) A B - B A B A - B (4) (5) B = s A is a vector with magnitude s A and is parallel to A if s is positive and antiparallel if s is negative.

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