If a , ~b and c are three unit vectors equally inclined to each other at an angle α. Then…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
If \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{~b}}\) and \(\stackrel{\rightharpoonup}{\mathrm{c}}\) are three unit vectors equally inclined to each other at an angle α. Then the angle between \(\stackrel{\rightharpoonup}{\mathrm{a}}\) and plane of \(\overrightarrow{\mathrm{b}}\) and \(\stackrel{\rightharpoonup}{\mathrm{c}}\) is
- θ = cos–1 \[\left(\frac{\cos \alpha}{\cos \frac{\alpha}{2}}\right)\]
- θ = sin–1 \[\left(\frac{\cos \alpha}{\cos \frac{\alpha}{2}}\right)\]
- θ = cos–1 \[\left(\frac{\sin \frac{\alpha}{2}}{\sin \alpha}\right)\]
- θ = sin–1 \[\left(\frac{\sin \frac{\alpha}{2}}{\sin \alpha}\right)\]
Answer
(A) θ = cos –1 ( 2 )
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