Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Equation of diagonal OG $\frac{x}{1}=\frac{y}{1}=\frac{z}{1}$ ⇒ point $B$ is $(1,1,0)$ ⇒ let $P$ be any point on diagonal OG $\therefore \mathrm{p}\equiv (\lambda ,\lambda ,\lambda )$ $\Rightarrow \mathrm{BP}\perp \mathrm{OD}$ $\therefore (\lambda -1)+(\lambda -1)+\lambda =0$ $\lambda =\frac{2}{3}$ $\therefore \mathrm{p}\equiv \left(\frac{2}{3},\frac{2}{3},\frac{2}{3}\right)$ $\mathrm{BP}=\sqrt{\frac{1}{9}+\frac{1}{9}+\frac{2}{9}}=\sqrt{\frac{4}{9}}=\sqrt{\frac{2}{3}}$