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JEE Main 202126 AugustEvening Shift
Exam
JEE Main
Year
2021
Date
26 August
Shift
Evening Shift
Subject
Mathematics
Chapter
Vector Algebra

JEE Main 2021 · 26 August · Evening Shift · Mathematics · Vector Algebra

A hall has a square floor of dimension 10m × 10m (see the figure)...

A hall has a square floor of dimension 10m×10m10m \times 10m (see the figure) and vertical walls. If the angle GPHGPH between the diagonals AGAG and BHBH is cos⁡−115,\cos^{- 1}\dfrac{1}{5}, then the height of the hall (in meters) is:

A hall has a square floor of dimension 10m × 10m (see the figure) and vertical walls. If the angle GPH between the

Options

  1. A525\sqrt{2}
  2. B535\sqrt{3}
  3. C5105\sqrt{10}
  4. D55

Correct answer

A. 525\sqrt{2}

Step-by-step solution

A hall has a square floor of dimension 10m × 10m (see the figure) and vertical walls. If the angle GPH between the

\overset{\to}{AG} = 10\overset{^}{i} + h\overset{^}{j} + 10\overset{^}{k}

\overset{\to}{BH} = - 10\overset{^}{i} + h\overset{^}{j} + 10\overset{^}{k}

cosθ=−100+h2+100(200+h2)2cos\theta = \dfrac{- 100 + {h}^{2} + 100}{{\left(\sqrt{200 + {h}^{2}}\right)}^{2}}

15=h2200+h2\dfrac{1}{5} = \dfrac{{h}^{2}}{200 + {h}^{2}}

200=4h2200 = 4{h}^{2}

h2=50{h}^{2} = 50

⇒h=52⇒ h = 5\sqrt{2}

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