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Question

ABC is a triangle where A=(2,3,5),B=(1,3,2) and C=(λ,5,μ). If the median through A is equally inclined with the axes, then

A
λ=14,μ=20
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B
λ=9,μ=6
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C
λ=72,μ=20
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D
λ=10,μ=7
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Solution

The correct option is A λ=9,μ=6
A is a median, then it meets BC at their mid-point D,
Coordinates of D are (λ12,4,2+μ2)
AD is equally inclined on the axes i.e. makes equal angle with all the three axes, which implies that, if l,m,n are the direction ratios then they should be equal.
λ12=4=2+μ2
λ=9,μ=6

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