Distance of the point P(-2,3,4) from the line x+23=2y+34=3z+45 measured parallel to the  plane 4x + 12y - 3z + 1 = 0 is d, then the value of (2d - 8).

Line through point P(-2,3,4) from the line x+23=2y+34=3z+45 is x+23=y+322=z+4353=λAny point on this line is Q3λ−2,2λ−32,53λ−43Direction ratios of PQ are 3λ,4λ−92,5λ+83Now PQ is parallel to the given plane  4x+12y−3z+1=0Hence, line is perpendicular to the normal to the plane. Thus,  4(3λ)+124λ−92−35λ+83=0 or  λ=2⇒ Q≡4,52,2⇒ PQ=(6)2+52−32+(6)2=172