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A B C D is parallelogram. The position vectors of A and C are respectively, 3 i +3 j +5 k and i -5 j -5 k . If M is the midpoint of the diagonal D B , then the magnitude of the projection of O M on O C , where O is the origin, is

Options

  1. A7 51
  2. B7 50
  3. C7 50
  4. D7 51

Correct answer

D. 7 51

Step-by-step solution

In a parallelogram, diagonals bisect each other. So, mid point of D B is also the midpoint of A C . Mid-point of M=2 i - j Direction ratio of O C=(1,-5,-5) Direction ratio of O M=(2,-1,0) Angle between O M and O C is given by . = (1 2+)-5(-1)(+-5) 0( 2^2+(-1)^2 ()^2+(-5)^2+(-5)^2 )() = 2+5 5 51 = 7 5 51 Projection of O M on O C is given by |O M| = 5 7 5 51 = 7 51

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