Mathematics - Vector Question with Solution | TestHub

$\begin{array}{rl}& \frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}+2}{-1}=\frac{\mathrm{z}+3}{2}=\lambda \text{ (let })\\ & (2\lambda +1,-\lambda -2,2\lambda -3)\\ & \because \overrightarrow{\mathrm{PA}}\cdot \overrightarrow{\mathrm{n}}=0\\ & \Rightarrow (2\lambda -1)2+(-\lambda +8)(-1)+(2\lambda -4)2=0\\ & \Rightarrow 4\lambda -2+\lambda -8+4\lambda -8=0\\ & \Rightarrow 9\lambda -18=0\Rightarrow \lambda =2\\ & \therefore \mathrm{A}(5,-4,1)\\ & \therefore \mathrm{AP}=\sqrt{3^2+6^2+0^2}=\sqrt{45}=3\sqrt{5}\end{array}$