Chapter 12, Problem 27CLT

To determine

To calculate: Intercepts and sketch or graph of the plane $3x-6y-12z=24$

Answer to Problem 27CLT

The x -axis intercept is $\left(8,0,0\right)$

The y -axis intercept is $\left(0,-4,0\right)$

The z -axis intercept is $\left(0,0,-2\right)$

Graph:

  

Explanation of Solution

Given information:

Equation of the plane:

  $3x-6y-12z=24$

Calculation:

To find the intercept on the x -axis put $y=z=0$

  $\begin{array}{l}3x-6\left(0\right)-12\left(0\right)=24\\ 3x=24\\ \boxed{x=8}\end{array}$

In coordinate form $\left(8,0,0\right)$

To find the intercept on the y -axis put $z=x=0$

  $\begin{array}{l}3\left(0\right)-6y-12\left(0\right)=24\\ -6y=24\\ \boxed{y=-4}\end{array}$

In coordinate form $\left(0,-4,0\right)$

To find the intercept on the z -axis put $x=y=0$

  $\begin{array}{l}3\left(0\right)-6\left(0\right)-12z=24\\ -12z=24\\ \boxed{z=-2}\end{array}$

In coordinate form $\left(0,0,-2\right)$

Graph: