Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Let $a,b,c$ be the intercepts on the coordinate axes and we have $a=b=c$. $\therefore \frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{a}}+\frac{\mathrm{z}}{\mathrm{a}}=1$ is required equation of plane. Since plane passes through point $(2,2,2)$, we write $\frac{2+2+2}{\mathrm{a}}=1\Rightarrow \mathrm{a}=6$ $\therefore$ Equation of plane is $\mathrm{x}+\mathrm{y}+\mathrm{z}=6$