Mathematics - Vector Question with Solution | TestHub

Equation of line through point $(-1,2,1)$ is $\to$$\begin{array}{rl}& \Rightarrow \frac{x+1}{2}=\frac{y-2}{3}=\frac{z-1}{4}=\lambda -(2)\\ & \text{So, }[\begin{array}{l}x=2\lambda -1\\ y=3\lambda +2\\ z=4\lambda +1\end{array}\end{array}$ $\mathrm{By}(1)\to \frac{x+2}{3}=\frac{y-3}{2}=\frac{z-4}{1}=\mu ($ Let $)$ So, $[\begin{array}{l}x=3\mu -2\\ y=2\mu +3\\ z=\mu +4\end{array}$ For intersection point ' P ' $\begin{array}{rl}& \mathrm{x}=2\lambda -1=3\mu -2\\ & \mathrm{y}=3\lambda +2=2\mu +3\\ & \mathrm{z}=4\lambda +1=\mu +4\end{array}$ So, point $\mathrm{P}(\mathrm{x},\mathrm{y},\mathrm{z})=(1,5,5)$ & $\mathrm{Q}(4,-5,1)$ $\begin{array}{rl}& \therefore PQ=\sqrt{9+100+16}\\ & =\sqrt{125}=5\sqrt{5}\end{array}$