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**Unformatted text preview: **Lecture 1: Three Dimensional Space and Vectors May 5, 2009 Lecture 1: Three Dimensional Space and Vectors Objectives Three-dimensional geometry concepts 1 Distance formula 2 Equations for special plane 3 Equation for spheres Vector concepts 1 Vector addition 2 Multiplication of scalars and vectors 3 Find unit vectors Lecture 1: Three Dimensional Space and Vectors Three dimensional geometry Lecture 1: Three Dimensional Space and Vectors Three dimensional geometry Need 3 numbers to describe position Lecture 1: Three Dimensional Space and Vectors Three dimensional geometry Need 3 numbers to describe position Distance d between points P 1 = ( x 1 , y 1 , z 1 ) and P 2 = ( x 2 , y 2 , z 2 ) is... Lecture 1: Three Dimensional Space and Vectors Three dimensional geometry Need 3 numbers to describe position Distance d between points P 1 = ( x 1 , y 1 , z 1 ) and P 2 = ( x 2 , y 2 , z 2 ) is... d = p ( x 1- x 2 ) 2 + ( y 1- y 2 ) 2 + ( z 1- z 2 ) 2 Lecture 1: Three Dimensional Space and Vectors Three dimensional geometry Need 3 numbers to describe position Distance d between points P 1 = ( x 1 , y 1 , z 1 ) and P 2 = ( x 2 , y 2 , z 2 ) is......

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