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બે સદિશો $\mathop P\limits^ \to $ અને $\mathop Q\limits^ \to $ એ એકબીજાને $ \theta $ ખૂણે છે. નીચેના પૈકી કયો એકમ સદિશ $\mathop P\limits^ \to $ અને $\mathop Q\limits^ \to $ ને લંબ છે.
$\frac{{\mathop P\limits^ \to \,\, \times \,\,\mathop Q\limits^ \to }}{{P.Q}}$
$\frac{{\hat P\,\, \times \,\,\hat Q}}{{\sin \,\,\theta }}$
$\frac{{\hat P\,\, \times \,\,\hat Q}}{{PQ\sin \,\,\theta }}$
$\frac{{\hat P\,\, \times \,\,\mathop Q\limits^ \to }}{{PQ\,\sin \,\,\theta }}$
Solution
Unit vector perpendicular to $\vec{P}$ and $\vec{Q}$ will be given as $\frac{\vec{P} \times \vec{Q}}{|\vec{P} \times \vec{Q}|}$
$=\frac{\overrightarrow{ P } \times \overrightarrow{ Q }}{ P Q \sin \theta}=\frac{\frac{\overrightarrow{ P }}{ P } \times \frac{\overrightarrow{ Q }}{ Q }}{\sin \theta}=\frac{\hat{ P } \times \hat{ Q }}{\sin \theta}$
