Question

Find the intercepts cut off by the plane $2x+y-z=5$.

Answer 1

Given, $2x+y-z=5$
$\Rightarrow \frac{2}{5}x+\frac{y}{5}-\frac{z}{5}=1$
$\Rightarrow \frac{x}{5/2}+\frac{y}{5}+\frac{z}{-5}=1$
It is known that the equation of a plane in intercept from is $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$, where $a,b,c$ are the intercepts cut off by the plane at $x,y$ and $z$ axes respectively.
Therefore, for the given equation,
$a=\frac{5}{2},b=5$ and $c=-5$
Thus, the intercepts cut off by the given plane are $\frac{5}{2},5$ and $-5$.