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

$\mathbf{OQ}=(1-3\mu )\mathbf{i}+(\mu -1)\mathbf{j}+(5\mu +2)\mathbf{k}$ and $\mathbf{OP}=3\hat{\mathbf{i}}+2\hat{\mathbf{j}}+6\hat{\mathbf{k}}$, where $O$ is origin. $$\begin{array}{rl}& \text{ Now, }\mathbf{PQ}=(1-3\mu -3)\hat{\mathbf{i}}+(\mu -1-2)\hat{\mathbf{j}}\\ & +(5\mu +2-6)\hat{\mathbf{k}}\\ & =(2-3\mu )\hat{\mathbf{i}}+(\mu -3)\hat{\mathbf{j}}+(5\mu -4)\hat{\mathbf{k}}\\ & \end{array}$$ $\because \mathbf{PQ}$ is parallel to the plane $$\begin{array}{rr}& x-4y+3z=1.\\ \therefore & -2-3\mu -4\mu +12+15\mu -12=0\\ \Rightarrow & 8\mu =2\Rightarrow \mu =\frac{1}{4}\end{array}$$