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Plane in space

A plane in space is determined by a point MATH in the plane and a vector MATH that is perpendicular to the plane. Equations of the plane through the point MATH perpendicular to the vector MATH may be written in the following forms:

General form: $ax+by+cz+d=0$

Vector equation: MATH

Scalar equation: MATH

Parametric equations: MATH (If $c=0$ and $b\neq 0$, let $z=t$ and solve for $y$, etc.)

A plane is also determined by a point MATH and two vectors $\QTR{bf}{u}$ and $\QTR{bf}{v}$ that lie in the plane but that are not parallel to each other.

Vector form: $\QTR{bf}{r+su+tv}$


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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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