AP EAMCET · Maths · Three Dimensional Geometry
If \(O(0,0,0), A(1,2,1), B(2,1,3)\) and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(O A B\) and edge \(B C\) is
- A \(\operatorname{Cos}^{-1}\left(\frac{6 \sqrt{2}}{5 \sqrt{7}}\right)\)
- B \(\operatorname{Sin}^{-1}\left(\frac{6 \sqrt{2}}{5 \sqrt{7}}\right)\)
- C \(\operatorname{Tan}^{-1}\left(\frac{6 \sqrt{2}}{5 \sqrt{7}}\right)\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(B) \(\operatorname{Sin}^{-1}\left(\frac{6 \sqrt{2}}{5 \sqrt{7}}\right)\)
Step-by-step Solution
Detailed explanation
\(\vec{OA} = (1,2,1)\), \(\vec{OB} = (2,1,3)\) \(\vec{n} = \vec{OA} \times \vec{OB} = (2 \cdot 3 - 1 \cdot 1)\mathbf{i} - (1 \cdot 3 - 1 \cdot 2)\mathbf{j} + (1 \cdot 1 - 2 \cdot 2)\mathbf{k} = (5, -1, -3)\) \(\vec{v} = \vec{BC} = C - B = (-1-2, 1-1, 2-3) = (-3, 0, -1)\)…
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