Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

If the given points be $\mathrm{A}(2,3,4)$ and $\mathrm{B}(6$, $7,8)$, then their mid-point $\mathrm{N}(4,5,6)$ must lie on the plane. The direction ratios of $AB$ are $4,4,4$, i.e. $1,1,1$.
$\therefore$ The required plane passes through $\mathrm{N}(4,5$, $6)$ and is normal to $\mathrm{AB}$. Thus its equation is $1(x-4)+1(y-5)+1(z-6)=0\Rightarrow x+y+z=15$