Let a, b ; and ; c be three unit vectors such that a ( b c ) = 3 … - Vidyadip

MCQ

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 :

✓
$\frac{{5\pi }}{6}$
B
$\frac{{2\pi }}{3}$
C
$\frac{{3\pi }}{4}$
D
$\frac{\pi }{2}$

✓

Answer

Correct option: A.

$\frac{{5\pi }}{6}$

a
$\left(\vec{a} \cdot \vec{c}-\frac{\sqrt{3}}{2}\right) \vec{b}-\left(\vec{a} \cdot \vec{b}+\frac{\sqrt{3}}{2}\right) \vec{c}=0$

$\Rightarrow \vec{a} \cdot \vec{b}=\cos \theta=-\sqrt{3} / 2 $

$\Rightarrow \theta=5 \pi / 6$

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