Teaching AWES Army Public School TGT Mock Test 2024 Mathematics Three Dimensional Geometry Angle with Planes
Find the angle between the line \(\vec r = \left( {3\hat i + \;\hat k} \right) + \lambda \;\left( {\;\hat j + \;\hat k} \right)\) and the plane \(\vec r \cdot \left( {2\hat i - \;\hat j + \;2\hat k} \right) = 1\) ?
1
\( {\sin ^{ - 1}}\left( {\frac{1}{{\sqrt 2 }}} \right)\)
2
\( {\sin ^{ - 1}}\left( {\frac{1}{{3}}} \right)\)
3
\( {\sin ^{ - 1}}\left( {\frac{1}{{3\sqrt 2 }}} \right)\)
4
None of these