The foot of the perpendicular from (0, 2, 3) to the line x+35=y−12=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=y−12=z+43=λ
Let P(5λ−3,2λ+1,3λ−4) be the foot of perpendicular of A(0, 2, 3). Then AP and given line are perpendicular to each other. ∴(5λ−3)5+(2λ−1)2+(3λ−7)3=0 ⇒38λ−38=0⇒λ=1.
Hence, P = (2, 3, –1)