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Question

The co-ordinates of the foot of perpendicular drawn from point P(1,0,3) to the line joining the points A(4,7,1) and B(3,5,3) is
  1. (5,7,1)
  2. (53,73,173)
  3. (23,53,73)
  4. (53,23,73)


Solution

The correct option is B (53,73,173)
Let D be the foot of perpendicular drawn from P(1,0,3) on the line AB joining (4, 7, 1) and (3, 5, 3). If D divides AB in ratio λ:1 then D=(3λ+4λ+1,5λ+7λ+1,3λ+1λ+1).....(i)

D.r's of PD are 2λ+3,5λ+7,2
D.r's of AB are -1, -2,2
PDAB;(2λ+3)2(5λ+7)4=0λ=74
Putting the value of λ in (i), we get the point D(53,73,173).

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