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Line

Some forms the equation for a line in the plane can take are:MATH

Some forms equations for a line in 3-dimensional space can take are:MATH

The equation for a line in the plane or in space can be written in vector formMATHwhere $\QTR{bf}{v}$ is a vector parallel to the line and MATH for $P$ some point on the line. Equations of the line through the point MATH or MATH parallel to the vector MATH or MATH may be written in the following forms:

Vector equation in the plane: MATH MATH

Vector equation in space: MATH MATH

If a line in space makes angles $\alpha $, $\beta $, $\gamma $ with the coordinate axes, then the vector MATH of direction cosines is parallel to the line and has length $1$.


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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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