First slide

Scalars and Vectors

Question

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

Easy

A

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

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

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

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

Solution

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

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