The Cartesian equation of a plane which passes through the points $\mathrm{A}(2,2,2)$ and making equal…
The Cartesian equation of a plane which passes through the points $\mathrm{A}(2,2,2)$ and making equal nonzero intercepts on the co-ordinate axes is
$x+y+z=6$
$x-2 y+z=0$
$2 x+y+z=7$
$x-y+z=6$
Solution
Let $a, b, c$ be the intercepts on the coordinate axes and we have $a=b=c$.
$\therefore \quad \frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{a}}+\frac{\mathrm{z}}{\mathrm{a}}=1$ is required equation of plane.
Since plane passes through point $(2,2,2)$, we write $\frac{2+2+2}{\mathrm{a}}=1 \Rightarrow \mathrm{a}=6$
$\therefore \quad$ Equation of plane is $\mathrm{x}+\mathrm{y}+\mathrm{z}=6$