Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Lines $\frac{2(x-2)}{\lambda }=\frac{y-1}{2}=\frac{z-3}{1}$ and $\frac{x-1}{1}=\frac{3\left(y-\frac{1}{3}\right)}{\lambda }=\frac{z-2}{1}$ are perpendicular to one another. $\begin{array}{rl}& \therefore \left(\frac{\lambda }{2}\right)(1)+(2)\left(\frac{\lambda }{3}\right)+(1)(1)=0\\ & \therefore \frac{\lambda }{2}+\frac{2\lambda }{3}=-1\Rightarrow \lambda =\frac{-6}{7}\end{array}$