Day 03 - Day 03 Spatial Descriptions 1 1/9/2012 Points and...

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Day 03 Spatial Descriptions 1/9/2012 1
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Points and Vectors 1/9/2012 2 point : a location in space vector : magnitude (length) and direction between two points p q v
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Coordinate Frames 1/9/2012 3 choosing a frame (a point and two perpendicular vectors of unit length) allows us to assign coordinates 0 p 0 q = = 1 2 0 0 0 q p v 0 ˆ x 0 ˆ y 0 o { } 0 = 5 . 1 2 0 q = 5 . 2 4 0 p
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Coordinate Frames 1/9/2012 4 the coordinates change depending on the choice of frame 1 p 1 q = = 2 1 1 1 1 q p v 1 ˆ x 1 ˆ y 1 o { } 1 = 2 5 . 0 1 q = 4 5 . 0 1 p
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Dot Product 1/9/2012 5 the dot product of two vectors = n u u u u 2 1 = n v v v v 2 1 v u v u v u v u v u T n n = + + + = 2 2 1 1 u v θ cos u cos v u v u =
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1/9/2012 6 suppose we are given
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Day 03 - Day 03 Spatial Descriptions 1 1/9/2012 Points and...

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