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Q88. Let ABC be a triangle with vertices at points A (2, 3, 5), B (−1, 3, 2) and C (λ, 5, μ) in three dimensional space. If the median through A is equally inclined with the axes, then (λ, μ) is equal to:

1. (10, 7)
2. (7, 5)
3. (7, 10)
4. (5, 7)

Correct answer: (7, 10)

Solution

The median through vertex A connects point A to the midpoint of side BC. For the median to be equally inclined with the axes, the direction ratios must be equal, which leads to the coordinates of point C being determined as (7, 10) to satisfy this condition.

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