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

Explanation

Let D be the foot of the perpendicular and let is divide BC in the ratio `lamda:1` . Then the coordinates of D are `(3lamda+4)/(lamda+1),(5lamda+7)/(lamda+1)and(3lamda+1)/(lamda+1)`.
Now, `" "vec(AD)botvec(BC)rArrvec(AD)*vec(BC)=0`
`rArr" "(2lamda+3)+2(5lamda+7)+4=0`
`or" "lamda=-(7)/(4)`
Thus, coordinates of D are `(5)/(3), (7)/(3) and (17)/(3)`.