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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

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.

2 y + z = 4

To determine

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

Explanation

Given information:

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

Formula used:

The two parallel lines intersect at infinity.

Calculation:

Consider equation of plane,

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

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

2y+(0)=4y=2

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

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

2(0)+z=4z=4

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

Since plane, 2y+z=4 parallel to x-axis but perpendicular to y-z plane.

Therefore, the plane, 2y+z=4 intersect at x-axis at infinity.

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

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

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

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