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# chap3 - Vectors Coordinate Systems Cartesian or...

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1 Vectors Coordinate Systems Cartesian or rectangular (x,y) Polar (r, θ )

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2 Transformations • What are the polar coordinates of the point ( x,y ) = (-3.50,-2.50) m ? Vectors and Scalars • A scalar quantity is specified by a single value and a unit but has no direction. (eg: temperature, volume, mass, speed, time intervals) • A vector quantity is specified by a number, an unit, and a direction . (velocity, displacement)
3 Are these four vectors equal? 1 2 3 252 9 38 1. Yes 2. No 3. I’m not sure! Vectors and Scalars • A generic vector has a magnitude and a direction • These four vectors are equal:

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4 Adding Vectors Geometrically • Laws of vector addition: A B B A a a a a + = + ( ) ( ) C B A C B A a a a a a a + + = + + Subtracting Vectors Geometrically ( ) B A B A a a a a - + = - ( ) A B A B a a a a = - +
Multiplying a Vector by a Scalar • If a vector A is multiplied by a positive scalar quantity m , the product vector m A has the same direction and the magnitude mA . • If

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chap3 - Vectors Coordinate Systems Cartesian or...

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