The perpendicular distance of P(1,2,3) from the line x−63=y−72=z−7−2 is

The point A(6,7,7) is on the lien. Let the perpendicular from P meet the line in L. Then AP2=(6−1)2+(7−2)2+(7−3)2=66. Also AL= projection of AP on line (actual d.c.'s 317,217,−217) =(6−7).317+(7−2).217+(7−3).−217 =17. ∴ ⊥ distance d of P from the line is given by d2=AP2−AL2=66−17=49, so that d=7 .