CALCULUS Understanding Its Concepts and Methods

Line

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

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

The equation for a line in the plane or in space can be written in vector formwhere is a vector parallel to the line and for some point on the line. Equations of the line through the point or parallel to the vector or may be written in the following forms:

Vector equation in the plane:

Vector equation in space:

If a line in space makes angles , , with the coordinate axes, then the vector of direction cosines is parallel to the line and has length .

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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.