The foot of the perpendicular from 2,−4,0to the join of 0,0,0 , 0,3,0 is

Equation of the line joining 0,0,0 , 0,3,0 isx0=y3=z0General point on the above line isQ0,3y1,0The direction ratios of the line joining  P2,−4,0 and Q0,3y1,0is−2,3y1+4,0Since the line PQ and x0=y3=z0are perpendicular to each other.33y1+4=0y1=−43 Therefore, the foot of the perpendicular of2,−4,0 to the join of 0,0,0 , 0,3,0 is Q0,−4,0