Chapter 12.5, Problem 36E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find an equation of the plane.

**36.** The plane that passes through the point (6, −1, 3) and contains the line with symmetric equations *x*/3 = *y* + 4 = *z*/2

To determine

**To find:** An equation of the plane that passes through the point

Explanation

**Formula:**

Write the expression to find equation of the plane through the point

The normal vector

Write the expressions for the symmetric equations for a line through the point

Write the symmetric equations of the line as follows.

Rewrite the symmetric equations as follows.

Compare equation (3) with (2) and write the point in the line and direction vector

Therefore the plane passes through the points

Write the expression to find direction vector from the point

Consider the vector from the point

**Calculation of vector**
**:**

Substitute 0 for

As both the vectors

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