Mathematics - Vector Question with Solution | TestHub

If the given points be $A(2,3,4)$ and $B$ $(6,7,8),$ then their mid-point $\mathrm{N}(4,5,6)$ must lie on the plane. The direction ratios of $\mathrm{AB}$ 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 $$1(x-4)+1(y-5)+1(z-6)=0\Rightarrow x+y+z=15$$