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JEE Main202126 Aug 2021Evening ShiftMathematicsVector AlgebraActual

A hall has a square floor of dimension 10 m × 10 m (see the figure) and vertical walls. If the angle G P H between the diagonals A G and B H is cos - 1 1 5 , then the height of the hall (in meters) is:

Options

  1. A5 2
  2. B5 3
  3. C5 10
  4. D5

Correct answer

A. 5 2

Step-by-step solution

AG → = 10 i ^ + h j ^ + 10 k ^ BH → = - 10 i ^ + h j ^ + 10 k ^ cos θ = - 100 + h 2 + 100 200 + h 2 2 1 5 = h 2 200 + h 2 200 = 4   h 2 h 2 = 50 ⇒ h = 5 2

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