# If $\vec {a}$ and $\vec {b}$ are two vectors, such that $\vec {a}.\vec {b}\le 0$ and $|\vec {a}\times \vec {b}$ then

If $\vec {a}$ and $\vec {b}$ are two vectors, such that $\vec {a}.\vec {b}\le 0$ and $|\vec {a}\times \vec {b}|$ then find the angle between $\vec {a}$ and $\vec {b}$

My Attempt:

Let $\theta$ be the angle between two vectors $\vec {a}$ and $\vec {b}$. Then, $$\cos \theta=\dfrac {\vec {a}.\vec {b}}{|\vec {a}|.|\vec {b}|}$$,

How do I proceed further now?

• Did you miss something? I mean theres no equation for crossproduct – Archis Welankar Apr 29 '17 at 12:40
• @ArchisWelankar, I didn't miss anything, rather the question is incomplete (I think)! – pi-π Apr 29 '17 at 12:43

## 1 Answer

Obviously Something's missing. One possibility is that you have $|a \times b|$ and $a.b$ So you can use this

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

• where does $\tan \theta$ come from? – pi-π Apr 29 '17 at 12:50
• @AlbertEinstein $|a \times b|=|a|.|b| \sin \theta$ – user441618 Apr 29 '17 at 12:53