Chapter 12.5, Problem 60E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find symmetric equations for the line of intersection of the planes.

*z* = 2*x* − *y* − 5, *z* = 4*x* + 3*y* − 5

To determine

**To find:** The symmetric equations for the line of intersection of the planes

Explanation

**Formula used:**

The symmetric equations of a line through the point

**Calculation:**

Write the equation of first plane as follows.

Write the equation of second plane as follows.

Consider a point on the line of intersection

Set

Substitute 0 for

Substitute 0 for

Substitute equation (4) in (5) and obtain the *x*- and *y*-coordinates as follows.

Therefore, the point on the line of intersection

The parallel direction vector is the cross product of normal vectors of both the planes.

The expression is also written as follows.

The normal vector

The normal vector of first plane is also written as follows.

The normal vector

The normal vector of second plane is also written as follows

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P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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