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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

A
(5,7,1)
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B
(53,73,173)
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C
(23,53,73)
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D
(53,23,73)
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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 ∵PD⊥AB;∴−(2λ+3)−2(5λ+7)−4=0⇒λ=−74 Putting the value of λ in (i), we get the point D(53,73,173).

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