Chapter 12.5, Problem 56E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one decimal place.)

5*x* + 2*y* + 3*z* = 2, *y* = 4*x* − 6*z*

To determine

Whether the planes

Explanation

If the two planes are parallel, the normal vector of one of the planes is the scalar multiple of normal vector of the other plane.

If the two planes are perpendicular to each other, the dot product of the normal vectors of the two planes is zero (the normal vectors of the planes must be orthogonal).

Write the equation of the first plane as follows:

Write the normal vector

The normal vector

Write the equation of the second plane as follows:

Rewrite the expression as follows:

Write the normal vector

The normal vector

From the normal vectors of the planes, it is clear that the normal vector of one of the plane is not the scalar multiple of other plane.

Therefore, the planes are not parallel.

Find the dot product of two planes

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