Official solution
\[{{x - 2} \over 3} = {{y + 1} \over 2} = {{z - 1} \over { - 1}} = \lambda \]
\[A(3\lambda + 2,2\lambda - 1, - \lambda + 1)\] line on 2x + 3y -z + 13 = 0
\[ \Rightarrow 2(3\lambda + 2) + 3(2\lambda - 1) - ( - \lambda + 1) + 13 = 0\]
\[ \Rightarrow 13\lambda + 13 = 0 \Rightarrow \lambda = - 1\]
Now point P(-1, -3, 2) lie on 3x + y + 4z = 16
\[ \Rightarrow 3(3\lambda + 2) + (3\lambda + 2) + 4(3\lambda + 2) = 16\]
\[ \Rightarrow 9\lambda + 6 + 2\lambda - 4\lambda - 1 + 4 = 16\]
\[ \Rightarrow 7\lambda = 7 \Rightarrow \lambda = 1\]
\[ \Rightarrow \] Q(5, 1, 0)
\[ \therefore \] PQ = \[\sqrt {36 + 16 + 4} = \sqrt {56} = 2\sqrt {14} \]