Find the coordinates of thefoot of the perpendicular drawn from point – InterviewSolution

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1.	Find the coordinates of thefoot of the perpendicular drawn from point `A(1,0,3)`to the join of points `B(4,7,1)a n d C(3,5,3)dot`
Answer» 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)`.

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