# CH3 - Chapter 3 Vectors Vectors and Scalars A scalar...

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Chapter 3 Vectors

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Vectors and Scalars A scalar quantity is completely specified by a single value with an appropriate unit and has no direction. A vector quantity is completely described by a number and appropriate units plus a direction. Can you answer first question on Objective test sheet?
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Vector Notation When handwritten, use an arrow: When printed, will be in bold print: A When dealing with just the magnitude of a vector in print, an italic letter will be used: A or | A | The magnitude of the vector has physical units The magnitude of a vector is always a positive number A
Vector Example A particle travels from A to B along the path shown by the dotted red line This is the distance traveled and is a scalar The displacement is the solid line from A to B The displacement is independent of the path taken between the two points Displacement is a vector

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Equality of Two Vectors Two vectors are equal if they have the same magnitude and the same direction A = B if A = B and they point along parallel lines All of the vectors shown are equal
Cartesian Coordinate System Also called rectangular coordinate system x - and y - axes intersect at the origin Points are labeled ( x , y )

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Polar Coordinate System Origin and reference line are noted Point is distance r from the origin in the direction of angle , counter clockwise from reference line Points are labeled ( r , )
Polar to Cartesian Coordinates Based on forming a right triangle from r and x = r cos y = r sin

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Cartesian to Polar Coordinates r is the hypotenuse and an angle must be ccw from positive x axis for these equations to be valid 2 2 tan y x r x y