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Two vectors $\vec{A}$ and $\vec{B}$ are inclined to each other at an angle $θ$ . Which of the following is the unit vector perpendicular to both $\vec{A}$ and $\vec{B}$ ?

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$\frac{\vec{A} \times \vec{B}}{\vec{A} . \vec{B}}$

$\frac{\hat{A} \times \hat{B}}{\sin θ}$

$\frac{\vec{A} \times \hat{B}}{A B \sin θ}$

$\frac{\hat{A} \times \vec{B}}{A B \cos θ}$

answer is B.

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Detailed Solution

$\hat{n} = \frac{\vec{A} \times \vec{B}}{A B \sin θ} = \frac{A \hat{A} \times B \hat{B}}{A B \sin θ} = \frac{\hat{A} \times \hat{B}}{\sin θ}$

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