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Question

The foot of the perpendicular from (0, 2, 3) to the line x+35=y12=z+43 is :

A
(3, 2, –1)
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B
(–2, 3, 4)
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C
(2, –1, 3)
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D
(2, 3, –1)
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Solution

The correct option is D (2, 3, –1)
x+35=y12=z+43=λ
Let P(5λ3,2λ+1,3λ4) be the foot of perpendicular of A(0, 2, 3). Then AP and given line are perpendicular to each other.
(5λ3)5+(2λ1)2+(3λ7)3=0
38λ38=0λ=1.
Hence, P = (2, 3, –1)

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