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JEE Main20265 April 2026Evening ShiftMathematicsVector AlgebraActual

Let O be the origin, OP = a and OQ = b . If R is the point on OP such that OP = 5 OR , and M is the point such that OQ = 5 RM , then PM is equal to :

Options

  1. A1 5 ( a - 4 b )
  2. B1 5 ( b - 4 a )
  3. C1 5 (- a + 4 b )
  4. D1 5 (- b + 4 a )

Correct answer

B. 1 5 ( b - 4 a )

Step-by-step solution

Given OP = a and OQ = b . Since OP = 5 OR , we have OR = a 5 . Also, OQ = 5 RM , which gives RM = b 5 . The position vector of M is given by OM = OR + RM = a 5 + b 5 . Now, we need to find PM : PM = OM - OP PM = ( a 5 + b 5 ) - a PM = b - 4 a 5 = 1 5 ( b - 4 a ) Answer: 1 5 ( b - 4 a )

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