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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 + y = 6

To determine

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

Explanation

Given information:

The equation of plane is x+y=6.

Calculation:

Consider equation of plane,

x+y=6 ...... (1)

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

x+0=6x=6

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

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

0+y=6y=6

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

Since plane, x+y=6 parallel to x-axis but perpendicular to y-x plane.

Therefore, the plane, x+y=6 intersect at z-axis at infinity.

There is no z-intercept.

Graph:

Consider the rectangular co-ordinate system x, y and z

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