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MHT CET20226 Aug 2022Morning ShiftMathematicsThree Dimensional GeometryActual

A vector a has components 2 p and 1 with respect to a rectangular Cartesian system. This system is rotated though a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, à has components p+1 and 1 , then

Options

  1. Ap=0
  2. Bp =-1 or p = 1 3
  3. Cp =1 or p =- 1 3
  4. Dp =1 or p =-1

Correct answer

C. p =1 or p =- 1 3

Step-by-step solution

Magnitude of a before rotation = Magnitude of a after rotation aligned & (2 p)^2+1^2=(p+1)^2+1^2 & 4 p^2+1=p^2+2 p+1+1 & 3 p^2-2 p-1=0 & p=1 or p= -1 3 aligned

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