If a , ~b , c are such that [ array lll a & b & c array ]=1, c = a b , a ~b < 2 3 and | a…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
If \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{~b}}, \overrightarrow{\mathrm{c}}\) are such that \(\left[\begin{array}{lll}
\vec{a} & \vec{b} & \vec{c}
\end{array}\right]=1, \vec{c}=\lambda \vec{a} \times \vec{b},\)
\(\overrightarrow{\mathrm{a}} \wedge \overrightarrow{\mathrm{~b}}\)< \(\frac{2 \pi}{3}\) and \(|\overrightarrow{\mathrm{a}}|=\sqrt{2},|\overrightarrow{\mathrm{~b}}|=\sqrt{3},\) \(|\overrightarrow{\mathrm{c}}|=\frac{1}{\sqrt{3}},\) then the angle between \(\stackrel{\rightharpoonup}{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) is
\(\overrightarrow{\mathrm{a}} \wedge \overrightarrow{\mathrm{~b}}\)< \(\frac{2 \pi}{3}\) and \(|\overrightarrow{\mathrm{a}}|=\sqrt{2},|\overrightarrow{\mathrm{~b}}|=\sqrt{3},\) \(|\overrightarrow{\mathrm{c}}|=\frac{1}{\sqrt{3}},\) then the angle between \(\stackrel{\rightharpoonup}{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) is
- \(\frac{\pi}{6}\)
- \(\frac{\pi}{4}\)
- \(\frac{\pi}{3}\)
- \(\frac{\pi}{2}\)
Answer
(B) 4
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