Question #a8907

Apr 11, 2017

$\text{ X-intercept="-6," Y-intercept="18," & Z-intercept=} - 9.$

Explanation:

Let us realise that the given eqn. represents a plane, say $\pi .$

The eqn. of a plane having the intercepts $a , b , c$ on the Axes, is,

$\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1. \ldots \ldots \ldots \ldots \ldots \left(\ast\right) .$

So, to determine the intercepts of $\pi ,$ let us convert in the $\left(\ast\right)$ form.

$3 x - y + 2 z = - 18.$

$\therefore \frac{3 x - y + 2 z}{-} 18 = 1 , i . e . , \frac{x}{-} 6 + \frac{y}{18} + \frac{z}{-} 9 = 1.$

$\Rightarrow \text{ X-intercept="-6," Y-intercept="18," & Z-intercept=} - 9.$