Direction ratios of the normal to the plane $\left(\overrightarrow{n}\right)=<\mathrm{1,1},1>$
Any general point on the given line is $\left(\lambda +1,\lambda -\mathrm{2,2}\lambda +3\right)$
From the diagram
$\left(\overrightarrow{AB}\right)=\left(\lambda ,\lambda -\mathrm{4,2}\lambda \right)$
$\overrightarrow{AB}.\overrightarrow{n}=0\Rightarrow \lambda +\lambda -4+2\lambda =0$
$\Rightarrow \lambda =1$
So, coordinates of the point $\mathrm{B}$ are $\left(2,-1,5\right)$
Hence, $AB=\sqrt{1+9+4}=\sqrt{14}$ units