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JEE Main2013MathematicsThree Dimensional GeometryActual

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

Options

  1. A(10,7)
  2. B(7,5)
  3. C(7,10)
  4. D(5,7)

Correct answer

C. (7,10)

Step-by-step solution

Since AD is the median D = ( -1 2 , 4, +2 2 ) Now, dR's of AD is a= ( -1 2 -2 )= -5 2 b=4-3=1, c= +2 2 -5= -8 2 Also, a, b, c are dR 's a=k l, b=k m, c=k n where l=m=n and l^2+m^2+n^2=1 l=m=n= 1 3 Now, a=1, b=1 and c=1 =7 and =10

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