Let v be a unit vector which follows the equation, v b = c Also, … - Vidyadip

MCQ

Let $\vec v$ be a unit vector which follows the equation, $\vec v \times \vec b = \vec c$ Also, $\left| {\vec b} \right| = 2$ and $\left| {\vec c} \right| = \sqrt 3 $ then

A
$\vec v = - \vec b + \vec b \times \vec c$
B
$\vec v = \frac{3}{4}(\vec b + 2\vec b \times \vec c)$
✓
$\vec v = \frac{1}{4}(\vec b + \vec b \times \vec c)$
D
$\vec v = \frac{{\vec b \times \vec c}}{4}$

✓

Answer

Correct option: C.

$\vec v = \frac{1}{4}(\vec b + \vec b \times \vec c)$

c
$\overrightarrow{\mathrm{b}} \times(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{b}})=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}$

$4 \vec{v}-(\vec{b} \cdot \vec{v}) \vec{b}=\vec{b} \times \vec{c}$

$|\vec{v} \times \vec{b}|=|\vec{c}|$

$\Rightarrow|\overrightarrow{\mathrm{v}}||\overrightarrow{\mathrm{b}}| \sin \theta=| \overrightarrow{\mathrm{q}}$

$2|\overrightarrow{\mathrm{v}}| \sin \theta=\sqrt{3}$

$\sin \theta=\frac{\sqrt{3}}{2}$

$\cos \theta=\frac{1}{2}$

$\Rightarrow 4 \vec{v}-\left(2 \times 1 \times \frac{1}{2}\right) \vec{b}=\vec{b} \times \vec{c}$

$\vec{v}=\frac{1}{4}(\vec{b}+\vec{b} \times \vec{c})$

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