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1E1 Lecture Notes 1: Vectors As an introduction to vectors we need to do some revision of coordinate geometry. 2D Coordinate Geometry O X Y x y y P (x, y) r θ 1 θ 2 The point  P  has coordinates ( x, y). The distance  OP  is  r  where r 2 =  x 2 + y 2 θ 1  is the angle between  OP  and the  X -axis. θ 2  is the angle between  OP  and the  Y -axis. Clearly cos θ 1  =  x r  and cos θ 2  =  y r  . These are called the direction cosines of the line OP , written as  l  and  m l  =  x r  m  =  y r 1

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