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Calculus / Calculus: Early Transcendentals 1 / Chapter 12.1 / Problem 22E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Properties of planes Find the points at which the

Chapter 12, Problem 22E

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QUESTION:

Properties of planes Find the points at which the following planes intersect the coordinate axes and find equations of the lines where the planes intersect the coordinate planes. Sketch a graph of the plane.

12x-9y+4z+72=0

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QUESTION:

Properties of planes Find the points at which the following planes intersect the coordinate axes and find equations of the lines where the planes intersect the coordinate planes. Sketch a graph of the plane.

12x-9y+4z+72=0

ANSWER:

Solution 22E

Step 1 of 5:

In this problem we need to find the at which the plane 12x − 9y + 4z + 72 = 0 intersect the coordinate axes and we have to find equations of the lines where the planes intersect the coordinate axes.

Let P be the plane described by the above equation.

$P:12x\ −\ 9y\ +\ 4z\ +\ 72\ =\ 0$

The point $(x,y,z)$ at which $P$ intersects the $x-$ axis must have $y=z=0$ .

Substitute $y=z=0$ into the equation of $P$ we get

$12x=\ -72$

$\Rightarrow{}x\ =\ -6$

so $P$ intersects the $x-$ axis at $(-6,0,0)$ .

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