Line through point P(−2,3,−4) and parallel to the given line x+23=2y+34=3z+45 is x+23=y+322=z+4353=λ
Any point on this line is Q[3λ−2,2λ−32,53λ−43]
Direction ratios of PQ are [3λ,4λ−92,5λ+83]
Now PQ is parallel to the given plane 4x+12y−3z+1=0
Hence, line is perpendicular to the normal to the plane.
Thus, 4(3λ)+12(4λ−92)−3(5λ+83)=0
or λ=2
⇒Q(4,52,2)
⇒PQ=√(6)2+(52−3)2+(6)2=172