Let D be the foot of the perpendicular and let it dividivide BC in the ratio k:1 then the coordinates of D are 3k+4/k+1,5k+7/k+1 ,3k+1/k+1 now,AD perpendicular to BC such that AD.BC=0 (2k+3)-2(5k+7)-4=0 such that k=-7/4 ,coor coordinates of D are (5/3,7/3,17/3)