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

Let $\Pi$ : $\mathrm{x}+\mathrm{y}-\mathrm{z}-4=0$ be the equation of a plane and A be the point with position $\hat{\mathrm{i}}+2\hat{\mathrm{j}}-3\hat{\mathrm{k}}$ vector . L is a line which passes through the point (1,2,3) with direction ratios 3,-1 and 4. If the distance of the point A from the line L measured parallel to the plane $\Pi$ is ${\mathrm{d}}_1$ and the distance of the point A from the plane $\Pi$ measured parallel to the line L is ${\mathrm{d}}_2$, then find the value of $\sqrt{{\mathrm{d}}_1^2-{\mathrm{d}}_2^2}$.