   Chapter 7.2, Problem 1E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Sketching a Plane in Space In Exercises 1-12, find the x-, y-, and z-intercepts of the plane. Then sketch the plane. See Example 1. x + y + z = 3

To determine

To calculate: The x-intercept, y-intercept and z-intercept of the plane, x+y+z=3 and sketch the plane.

Explanation

Given information:

The equation of plane is x+y+z=3.

Formula used:

The general equation of plane,

ax+by+cz=d

The x-intercept of the plane, ax+by+cz=d can be calculated by substituting 0 for y and 0 for z, the y-intercept of the plane, ax+by+cz=d can be calculated by substituting 0 for x and 0 for z and the z-intercept of the plane, ax+by+cz=d can be calculated by substituting 0 for x and 0 for y, where a, b and c not all zero.

Calculation:

Consider equation of plane,

x+y+z=3 ...... (1)

Substitute, 0 for y and 0 for z in equation (1).

x+0+0=3x=3

Hence, the x-intercept of the plane, x+y+z=3 is (3,0,0).

Substitute, 0 for x and 0 for z in equation (1).

0+y+0=3y=3

Hence, the y-intercept of the plane, x+y+z=3 is (0,3,0).

Substitute, 0 for x and 0 for y in equation (1).

0+0+z=3z=3

Hence, the z-intercept of the plane, x+y+z=3 is (0,0,3)

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