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JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec a,\vec b\;\) and \(\;\vec c\) be three unit vectors such that \(\vec a \times \left( {\vec b \times \vec c} \right) = \frac{{\sqrt 3 }}{2}\left( {\vec b + \vec c} \right)\) . If \(\vec b\) is not parallel to \(\vec c\) then angle between \(\vec a\;\) and \(\;\vec b\) is :
- A \(\frac{{5\pi }}{6}\)
- B \(\frac{{2\pi }}{3}\)
- C \(\frac{{3\pi }}{4}\)
- D \(\frac{\pi }{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{{5\pi }}{6}\)
Step-by-step Solution
Detailed explanation
\(\left(\vec{a} \cdot \vec{c}-\frac{\sqrt{3}}{2}\right) \vec{b}-\left(\vec{a} \cdot \vec{b}+\frac{\sqrt{3}}{2}\right) \vec{c}=0\) \(\Rightarrow \vec{a} \cdot \vec{b}=\cos \theta=-\sqrt{3} / 2 \) \(\Rightarrow \theta=5 \pi / 6\)
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