JEE Mains · Maths · STD 12 - 10. vector algebra
A hall has a square floor of dimension \(10\, \mathrm{~m} \times 10\, \mathrm{~m}\) (see the figure) and vertical walls. If the angle \(GPH\) between the diagonals \(\mathrm{AG}\) and \(\mathrm{BH}\) is \(\cos ^{-1} \frac{1}{5}\), then the height of the hall (in \(meters\)) is :
- A \(5\)
- B \(2 \sqrt{10}\)
- C \(5 \sqrt{3}\)
- D \(5 \sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(5 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{A}(\hat{\mathrm{j}}) \cdot \mathrm{B}(10 \hat{\mathrm{i}})\) \(H(h\hat{\mathrm{j}}+10 \hat{\mathrm{k}})\) \(G(10 \hat{\mathrm{i}}+\mathrm{h} \hat{\mathrm{j}}+10 \hat{\mathrm{k}})\) \(\overline{\mathrm{AG}}=10 \hat{\mathrm{i}}+\mathrm{hj}+10 \hat{\mathrm{k}}\)…
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