MCQ
Which of the following is the unit vector perpendicular to $\overrightarrow A $ and $\overrightarrow B $
  • A
    $\frac{{\hat A \times \hat B}}{{AB\,\sin \theta }}$
  • B
    $\frac{{\hat A \times \hat B}}{{AB\,\cos \theta }}$
  • $\frac{{\overrightarrow A \times \overrightarrow B }}{{AB\,\sin \theta }}$
  • D
    $\frac{{\overrightarrow A \times \overrightarrow B }}{{AB\,\cos \theta }}$

Answer

Correct option: C.
$\frac{{\overrightarrow A \times \overrightarrow B }}{{AB\,\sin \theta }}$
c
(c) Vector perpendicular to $A$ and $B$, $\vec A \times \vec B = AB\sin \theta \;\hat n$

$\therefore$ Unit vector perpendicular to $A$ and $B$
$\hat n = \frac{{\vec A \times \vec B}}{{|\vec A| \times |\vec B|\sin \theta }}$

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