Chapter 12.5, Problem 57E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

(a) Find parametric equations for the line of intersection of the planes and (b) find the angle between the planes.

*x* + *y* + *z* = 1, *x* + 2*y* + 2*z* = l

(a)

To determine

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

Explanation

**Formula:**

Write the expressions to find the parametric equations for a line through the point

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

**Calculation of point on the line of intersection of planes:**

Substitute 0 for

Solve equations (4) and (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.

Write the normal vector

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

Write the normal vector

(b)

To determine

**To find:** The angle between the planes

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