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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 + 2 y + z = 4

To determine

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

Explanation

Given information:

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

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,

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

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

x+0+0=4x=4

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

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

0+2y+0=4y=2

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

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

0+0+z=4z=4

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

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