Let a , ~b and c be non–coplanar unit vectors equally inclined to one another at an acute…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
Let \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{~b}}\) and \(\stackrel{\rightharpoonup}{\mathrm{c}}\)be non–coplanar unit vectors equally inclined to one another at an acute angle θ. Then \(\left[\begin{array}{lll}
\overrightarrow{\mathrm{a}} & \overrightarrow{\mathrm{~b}} & \overrightarrow{\mathrm{c}}
\end{array}\right]\) in terms of θ is equal to :
- \((1+\cos \theta) \sqrt{\cos 2 \theta}\)
- \((1+\cos \theta) \sqrt{1-2 \cos 2 \theta}\)
- \((1-\cos \theta) \sqrt{1+2 \cos \theta}\)
- none of these
Answer
(C) (1- ) 1+2
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