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QJEEM16Ma9edb: JEE Main 2016 Mathematics - Class 12 JEEM16Ma9edb Solution: ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, …

ABC is a triangle in a plane with vertices

A(2, 3, 5), B(−1, 3, 2) and C( λ\lambda , 5, μ\mu ).

If the median through A is equally inclined to the coordinate axes, then the value of ( λ\lambda 3 + μ\mu 3 + 5) is :

Multiple Choice Options

  • A 1130
  • B 1348
  • C 676
  • D 1077

Step-by-Step Verified Solution

JEE Main 2016 (Online) 10th April Morning Slot Mathematics - 3D Geometry Question 286 English Explanation

DR's of AD are

λ−12−2,5+32−3,μ+22−5{{\lambda - 1} \over 2} - 2,{{5 + 3} \over 2} - 3,{{\mu + 2} \over 2} - 5

i.e.   λ−52,  1,  μ−82{{\lambda - 5} \over 2},\,\,1,\,\,{{\mu - 8} \over 2}

As medium is making equal angles with coordinate axes,

∴\therefore     λ−52=1=μ−82{{\lambda - 5} \over 2} = 1 = {{\mu - 8} \over 2}

⇒\Rightarrow     λ\lambda = 7,    μ\mu = 10

∴\therefore     λ\lambda 3 + μ\mu 3 + 5 = 73 + 103 + 5 = 1348

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