Distance - DISTANCES Math21a Fall 2006 DISTANCE POINT-POINT If P and Q are two points then d P Q = | vector PQ | is the distance between P and Q

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Unformatted text preview: DISTANCES Math21a, Fall 2006 DISTANCE POINT-POINT. 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 POINT-PLANE. 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 POINT-LINE. 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 LINE-LINE. 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.

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