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AP EAMCET20224 Jul 2022Morning ShiftMathematicsThree Dimensional GeometryActual

If the point a , 8 , - 2 divides the line segment joining the points 1 , 4 , 6 and 5 , 2 , 10 in the ratio m : n then 2 m n - a 3 =

Options

  1. A- 7
  2. B1
  3. C- 2
  4. D3

Correct answer

B. 1

Step-by-step solution

Given, The point a ,   8 , - 2 divides the line segment joining the points 1 , 4 , 6 and 5 , 2 , 10 in the ratio m : n , So, by section formula we get, a = 5 m + n m + n   . . . . . . 1 8 = 2 m + 4 n m + n   . . . . . . . 2   - 2 = 10 m + 6 n m + n   . . . . . . . . . . 3 Now solve either equation 2   or  3 we get, m n = - 2 3 Now putting in equation 1 we get a = - 7 , Now putting the values in 2 m n - a 3 = - 2 × 2 3 - - 7 3 = 7 - 4 3 = 1 .

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