The foot of the perpendicular from (5,7,3) to the join of (9,13,15), (12,21,10) is

Let A(5,7,3),B(9,13,15),C(12,21,10)Let P be the foot of the perpendicular from A to BC↔.Let P divides BC↔ in the ratio k:1∴P=9+12k1+k,13+21kk+1,15+10k1+kD.r’s of AP↔ are  9+12k1+k−5,13+21kk+1−7,15+10k1+k−3D.r’s of BC↔ are (12−9,21−13,10−15)=(3,8,−5)AP↔⊥BC↔⇒39+12k1+k−5+813+21k1+k−7 ⇒−515+10k1+k−3=0∴ Foot of the perpendicular P=(9,13,15),