Mathematics - Vector Question with Solution | TestHub

Let feet of perpendicular is $(2\alpha ,3\alpha +2,4\alpha +3)$ $\Rightarrow$ Direction ratio of the $\perp$ line is $2\alpha -3,3\alpha +3,4\alpha -8$. and $\Rightarrow$ Direction ratio of the line are $2,3,4$ $\Rightarrow 2(2\alpha -3)+3(3\alpha +3)+4(4\alpha -8)=0$ $\Rightarrow \alpha =1$ $\Rightarrow$ Feet of $\perp$ is $(2,5,7)$ $\Rightarrow$ Length $\perp$ is $\sqrt{1^2+6^2+4^2}=\sqrt{53}$