Let a be a unit vector perpendicular to unit vectors b and c and … - Vidyadip

MCQ

Let $\overline{ a }$ be a unit vector perpendicular to unit vectors $\bar{b}$ and $\bar{c}$ and if the angle between $\bar{b}$ and $\bar{c}$ is $\alpha$, then $\bar{b} \times \bar{c}$ is

A
$\pm(\cos \alpha) \bar{a}$
B
$\pm(\operatorname{cosec} \alpha) \bar{a}$
✓
$\pm(\sin \alpha) \overline{ a }$
D
none of these

✓

Answer

Correct option: C.

$\pm(\sin \alpha) \overline{ a }$

(C) Here, $\overline{ a }= \pm \frac{\overline{ b } \times \overline{ c }}{|\overline{ b } \times \overline{ c }|}$
$\Rightarrow \overline{ b } \times \overline{ c }= \pm|\overline{ b } \times \overline{ c }| \overline{ a }$
$= \pm(\sin \alpha) \overline{ a } \ldots[\because|\overline{ b } \times \overline{ c }|=\sin \alpha]$

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