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Q.

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

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a

$λ = - 7, μ = - 10$

b

$λ = 7, μ = 10$

c

$λ = - 10, μ = 7$

d

$λ = 10, μ = 7$

answer is C.

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Detailed Solution

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$M (\frac{- 1 + λ}{2}, \frac{3 + 5}{2}, \frac{2 + μ}{2}) \Rightarrow M (\frac{- 1 + λ}{2}, 4, \frac{2 + μ}{2}) \begin{array}{r} d.r's of \bar{AM} = (\frac{- 1 + λ}{2} - 2,4 - 3, \frac{2 + μ}{2} - 5) = (\frac{λ - 5}{2}, 1, \frac{μ - 8}{2}) \end{array} Equally Inclined \Rightarrow \frac{λ - 5}{2} = 1 = \frac{μ - 8}{2} \Rightarrow λ = 7, μ = 10$

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