Unformatted text preview: An immediate corollary of Remark 1.5.1 is Corollary 1.5.2. The planes given by two linear equations A 1 x + B 1 y + C 1 z = D 1 A 2 x + B 2 y + C 2 z = D 2 are parallel (or coincide) precisely if the two normal vectors −→ N 1 = A 1 −→ ı + B 1 −→ + C 1 −→ k −→ N 2 = A 2 −→ ı + B 2 −→ + C 2 −→ k are (nonzero) scalar multiples of each other; when the normal vectors are equal (i.e., the two lefthand sides of the two equations are the same) then the planes coincide if D 1 = D 2 , and otherwise they are parallel and nonintersecting....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Vectors

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