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JEE Main2016MathematicsThree Dimensional GeometryActual

A B C 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 λ 3 + μ 3 + 5 is

Options

  1. A1130
  2. B1348
  3. C1077
  4. D676

Correct answer

B. 1348

Step-by-step solution

Let coordinate of mid-point of B C is point D , then D ≡ λ - 1 2 ,   4 ,   μ + 2 2 And, A ≡ 2 , 3 , 5 Therefore, direction ratios of A D are λ - 1 2 - 2 ,   4 - 3 , μ + 2 2 - 5 λ - 5 2 ,   1 , μ - 8 2 Hence, direction cosines of A D are λ - 5 2 λ - 5 2 2 + 1 + μ - 8 2 2 ,   1 λ - 5 2 2 + 1 + μ - 8 2 2 , μ - 8 2 λ - 5 2 2 + 1 + μ - 8 2 2 Since, median A D is making equal angles with coordinate axes, therefore &

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