First slide

Vectors

Question

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

Moderate

A

$\frac{\hat{A} \times \hat{B}}{ABsinθ}$
B

$\frac{\hat{A} \times \hat{B}}{ABcosθ}$
C

$\frac{\vec{A} \times \vec{B}}{ABsinθ}$
D

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

Solution

Vector perpendicular to A and B. $\vec{A} \times \vec{B} = ABsinθ \hat{n}$
$∴$ Unit vector perpendicular to A and B
$\hat{n} = \frac{\vec{A} \times \vec{B}}{| \vec{A} | \times | \vec{B} | sinθ}$

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