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JEE Main 2016 · 10 Apr · Shift 1, Mathematics question 83

ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C(λ, 5, μ). If the median through A is equally inclined to the coordinate axes, then the value of (λ3+μ3+5)(\lambda^3+\mu^3+5) is :

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Answer and worked solution

Official answer: B

The midpoint of BC is (λ−12,4,μ+22)\left(\frac{\lambda-1}2,4,\frac{\mu+2}2\right), so the median's direction is (λ−52,1,μ−82)\left(\frac{\lambda-5}2,1,\frac{\mu-8}2\right). Equal inclination to the axes (taking all components equal) gives λ = 7, μ = 10, and λ3+μ3+5=1348\lambda^3+\mu^3+5=1348.

Topics:Direction cosines and ratios
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