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JEE Main202118 Mar 2021Morning ShiftMathematicsVector AlgebraActual

A vector a → has components 3 p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, a → has components p + 1 and 10 , then a value of p is equal to:

Options

  1. A1
  2. B- 5 4
  3. C4 5
  4. D- 1

Correct answer

D. - 1

Step-by-step solution

a → Old = 3 p i ^ + j ^ a → New = ( p + 1 ) i ^ + 10 j ^ ⇒ a → Old = a → New ⇒ 9 p 2 + 1 = p 2 + 2 p + 1 + 10 8 p 2 - 2 p - 10 = 0 4 p 2 - p - 5 = 0 ( 4 p - 5 ) ( p + 1 ) = 0 ⇒ p = 5 4 , - 1

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