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MHT CET20244 May 2024Morning ShiftMathematicsVector AlgebraActual

Let p and q be the position vectors of P and Q respectively, with respect to O and | p |= p ,| q |= q . The points R and S divide PQ internally and externally in the ratio 2: 3 respectively. If O R and OS are perpendiculars, then

Options

  1. A9 p ^2=4 q ^2
  2. B4 p ^2=9 q ^2
  3. C9 p =4 q
  4. D4 p =9 q

Correct answer

A. 9 p ^2=4 q ^2

Step-by-step solution

Let r and s be the position vectors of points R and S respectively. r = 3 p +2 q 3+2 and s = 3 p -2 q 3-2 As OS and OR are perpendicular, we get r s =0 aligned & ( 3 p+2 q 5 ) ( 3 p-2 q 1 )=0 & 9 p^2-6 p q+6 p q-4 q^2=0 & 9 p^2=4 q^2 aligned

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