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Unformatted text preview: DISTANCES Math21a, Fall 2006 DISTANCE POINTPOINT. If P and Q are two points, then d ( P, Q ) =  vector PQ  is the distance between P and Q . Unlike the book, we write  vectorv  =  vectorv  in this handout. DISTANCE POINTPLANE. If P is a point in space and Σ : vectorn · vectorx = d is a plane containing a point Q , then d ( P, Σ) =  vector PQ · vectorn   vectorn  is the distance between P and the plane. Proof: use the angle formula. DISTANCE POINTLINE. If P is a point in space and L is the line vector r ( t ) = Q + tvectoru , then d ( P, L ) =  ( vector PQ ) × vectoru   vectoru  is the distance between P and the line L . Proof: the area divided by base length is height of parallelogram. DISTANCE LINELINE. L is the line vector r ( t ) = Q + tvectoru and M is the line vectors ( t ) = P + tvectorv , then d ( L, M ) =  ( vector PQ ) · ( vectoru × vectorv )   vectoru × vectorv  is the distance between the two lines L and M . Proof: the distance is the length of the vector projection of...
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This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.
 Spring '08
 Skrypka
 Math, Calculus

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