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MathsJEE Main 2 Apr 2026, Shift 2·Q16·MCQ·Moderate

Vectors · Angle between two vectors

Two adjacent sides of a parallelogram PQRSPQRS are given by PQ→=j^+k^\overrightarrow{PQ} = \hat j + \hat k and PS→=i^−j^\overrightarrow{PS} = \hat i - \hat j. If the side PSPS is rotated about the point PP by an acute angle α\alpha in the plane of the parallelogram so that it becomes perpendicular to the side PQPQ, then sin⁡2(5α2)−sin⁡2(α2)\sin^2\left(\dfrac{5\alpha}{2}\right) - \sin^2\left(\dfrac{\alpha}{2}\right) is equal to:
  1. (1)12\dfrac12
  2. (2)32\dfrac{\sqrt3}{2}
  3. (3)34\dfrac{\sqrt3}{4}
  4. (4)235\dfrac{2\sqrt3}{5}

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