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

A point $(3\lambda +1,\lambda +2,2\lambda +3)$ of the first line lies on the second line when $\frac{3\lambda +1-3}{1}=\frac{\lambda +2-1}{2}=\frac{2\lambda +3-2}{3}$, giving $\lambda =1$. The point of intersection is $P(4,3,5)$. The plane at the greatest distance from O through P is perpendicular to $\mathrm{OP}:4x+3y+5z=50$.