Chapter 11, Problem 16CLT

To determine

To Graph:

The graph of the plane.

Explanation of Solution

Given Information:

Equation: $3x-6y-12z=24$

Consider the following equation.

  $3x-6y-12z=24$

To sketch the trace of the function using graphing Maple.

  

The above graph is graph of the plane given by $3x-6y-12z=24$ .

To label the intercepts, proceed as follows:

First get the points at which the plane meets the axes.

So, the observation are as follows:

The plane meets the $x-$ axis at $x=6$

Hence the $x-$ intercepts is $\left(6,0,0\right)$

The plane meets the $y-$ axis at $y=-4$

Hence the $y-$ intercepts is $\left(0,-4,0\right)$

The plane meets the $z-$ axis at $z=-2$

Hence the $z-$ intercepts is $\left(0,0,-2\right)$

  

Above graph shows the points at which the plane meets the axes.