Question

If $\theta$ is the angle between $\overline{a}$ and $\overline{b}$, then $\frac{|\overline{a}\times \overline{b}|}{\overline{a}\cdot \overline{b}}$ equals

• A. $\tan \theta$
• B. $-\tan \theta$
• C. $\cot \theta$
• D. $-\cot \theta$

Answer 1

Answer: (A)

$\tan \theta$

We know

$|a\times b|=|a||b|\sin \theta$

and
$a.b=|a||b|\cos \theta$

Taking the ration of the above two, we get

$\frac{|a\times b|}{a.b}=\tan \theta$