Unformatted text preview: p = D − D = 0 . Thus, letting the second point P 1 be an arbitrary point P ( x,y,z ) in the plane, we have Remark 1.5.1. If P ( x ,y ,z ) is any point whose coordinates satisfy ( 1.21 ) Ax + By + Cz = D then the locus of Equation ( 1.21 ) is the plane through P perpendicular to the normal vector −→ N := A −→ ı + B −→ + C −→ k . This geometric characterization of a plane from an equation is similar to the geometric characterization of a line from its parametrization: the normal vector −→ N formed from the left side of Equation ( 1.21 ) (by analogy with the direction vector −→ v of a parametrized line) determines the “tilt” of...
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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, Dot Product

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