Question

Which of the following is the unit vector perpendicular to $\vec{A}$ and $\vec{B}$ ?

• A. $\frac{\hat{A} \times \hat{B}}{A B \sin \theta}$
• B. $\frac{\hat{A} \times \hat{B}}{A B \cos \theta}$
• C. $\frac{\vec{A} \times \vec{B}}{A B \sin \theta}$
• D. $\frac{\vec{A} \times \vec{B}}{A B \cos \theta}$

Answer 1

Answer: (C)

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