Find the foot of the perpendicular drawn from the point A(1,0,3) to the join of the points B(4,7,1) and C(3,5,3)

Hello student,
Please find the answer to your question below
Let ‘L’ be the fot of perpendicular AL, which divides BC in the ratio a:1 =
(3a+4)/(a+1),(5a+7)/(a+1),(3a+1)/(a+1)
Also D.R’s of the BC and AL are ,
D.R’s of BC= -1,-2,2
D.R’s of AL =((3a+4)/(a+1))-1,((5a+7)/(a+1))-0,((3a+1)/(a+1))-3
since AL is perpendicular to BC
Cos90 = 0 →BC, AL are the lines with D.R’s as magnitudes
2(((3a+4)/(a+1))-1)-2(((5a+7)/(a+1))-0)+(((3a+1)/(a+1))-3)2=0
we get a=-7/4
So L=(5/3,7/3,17/3)