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Multiplication with Vectors

Which of the ...

Question

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

A

\frac{^A \times^B}{A B sin θ}

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B

\frac{^A \times^B}{A B cos θ}

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C

\frac{\to A \times \to B}{A B sin θ}

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D

\frac{\to A \times \to B}{A B cos θ}

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Solution

The correct option is C $\frac{\to A \times \to B}{A B sin θ}$
Vector perpendicular to $\to A$ and $\to B$ can be given as
$\to A \times \to B = A B sin θ^n$
∴ Unit vector perpendicular to $\to A$ and $\to B$ is given by $^n = \frac{\to A \times \to B}{A B sin θ}$

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