Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Length of $\perp$ er from the point $A(\bar{a})$ to the plane $\bar{r}\cdot \bar{n}=p$ is $\frac{|\bar{a}\cdot \bar{n}-p|}{|\bar{n}|}$ Here $\overline{\mathrm{a}}=0\hat{\mathrm{i}}+0\hat{\mathrm{j}}+0\hat{\mathrm{k}}$ and $\overline{\mathrm{n}}=\hat{\mathrm{i}}-2\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ $\therefore \overline{\mathrm{a}}\cdot \overline{\mathrm{n}}=0$ and $|\overline{\mathrm{n}}|=\sqrt{1+4+9}=\sqrt{14}$ Hence required distance is $\frac{|0-14|}{\sqrt{14}}=\sqrt{14}$