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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 15-18, find the x-, y-, and z-intercepts of the plane. Then sketch the plane.

4 x y + 2 z = 8

To determine

To calculate: The x-intercept, y-intercept and z-intercept of the plane, 4xy+2z=8 and sketch the plane.

Explanation

Given information:

The equation of plane is 4xy+2z=8.

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,

4xy+2z=8 ...... (1)

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

4x(0)+2(0)=8x=2

Hence, the x-intercept of the plane, 4xy+2z=8 is (2,0,0).

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

4(0)y+2(0)=8y=8

Hence, the y-intercept of the plane, 4xy+2z=8 is (0,8,0).

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

4(0)(0)+2z=8z=4

Hence, the z-intercept of the plane, 4xy+2z=8 is (0,0,4)

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