The correct option is
C √53 units
The general point on the line x2=y−23=z−34 is (x,y,z)=(2λ,3λ+2,4λ+3)
Let Q(x,y,z)=(2λ,3λ+2,4λ+3)
The directional cosines of PQ=2λ−3,3λ+3,4λ−8
Since the line L and PQ are perpendicular
(2λ−3)(2)+(3λ+3)(3)+(4λ−8)4=0⟹λ=1⟹Q(2,5,7)
The length of the line segment PQ=√(3−2)2+(−1−5)2+(11−7)2=√53