Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The co-ordinates of foot of perpendicular can be obtained by $\begin{array}{rl}& \frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}=\frac{-\left(a_1+b{y}_1+c_1-d\right)}{a^2+b^2+c^2}\\ & \Rightarrow \frac{x-0}{2}=\frac{y-0}{6}=\frac{z-0}{-3}=\frac{-(2\times 0+6\times 0-3\times 0-63)}{2^2+6^2+(-3{)}^2}\\ & \Rightarrow \frac{x}{2}=\frac{y}{6}=\frac{z}{-3}=\frac{63}{49}\\ & \Rightarrow x=\frac{18}{7},y=\frac{54}{7},z=\frac{-27}{7}\\ & \Rightarrow \left(\frac{18}{7},\frac{54}{7},\frac{-27}{7}\right)\end{array}$