   Chapter 7.2, Problem 3E ### 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. 4 x + 2 y + 6 z = 12

To determine

To calculate: The x-intercept, y-intercept and z-intercept of the plane, 4x+2y+6z=12 and sketch the plane.

Explanation

Given information:

The equation of plane is 4x+2y+6z=12.

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.

Calculation:

Consider equation of plane,

4x+2y+6z=12 ...... (1)

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

4x+2(0)+6(0)=124x=12x=3

Hence, the x-intercept of the plane, 4x+2y+6z=12 is (3,0,0).

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

4(0)+2y+6(0)=122y=12y=6

Hence, the y-intercept of the plane, 4x+2y+6z=12 is (0,6,0).

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

4(0)+2y(0)+6z=126z=12z=2

Hence, the z-intercept of the plane, 4x+2y+6z=12 is (0,0,2)

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