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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

∆ A B C has vertices at A ≡ 2 , 3 , 5 , B ≡ ( - 1 , 3 , 2 ) and C ≡ λ , 5 , μ . If the median through A is equally inclined to the axes, then the values of λ and μ respectively are

Options

  1. A10 , 7
  2. B9 , 10
  3. C7 , 9
  4. D7 , 10

Correct answer

D. 7 , 10

Step-by-step solution

D = λ - 1 2 , 5 + 3 2 , μ + 2 2 = λ - 1 2 , 4 , μ + 2 2 Direction ratios of AD are ( λ - 1 2 , - 2 , 4 - 3 , μ + 2 2 - 5 ) i . e .( λ - 1 - 4 2 , 1 , μ + 2 - 10 2 ) i . e .( λ - 5 2 , 1 , μ + 8 2 ) Now if we go by options (since the line AD is equally inclined to coordinate axes, its direction ratio are in ratio ( ± 1 : ± 1 : ± 1 ) We get that for λ = 7 , μ = 10 direction ratios of AD are 1,1,1 .

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