$A = (2, 3, 5); B = (- 1, 3, 2); C = (λ, 5, μ)$ are the vertices of a triangle. If the median AM is equally inclined to the coordinate axes, then $(λ, μ)$

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(10,7)

(–10,7)

(7,10)

(–7,–10)

answer is C.

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Detailed Solution

$D = mid point of BC = (\frac{λ - 1}{2}, 4, \frac{M + 2}{2}) AD = (\frac{λ - 1}{2} - 2, 4 - 3, \frac{M + 2}{2} - 5) given equally inclined coordinate axes \Rightarrow \frac{x - 5}{2} = 1 = \frac{M - 8}{2} \Rightarrow λ = 7 M = 10$

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