Given two vectors, how can I denote the angle between them?

Question

Given the vectors $\vec{a}$ and $\vec{b}$, how can I denote the angle between them?

Answer 1

The angle symbol is $\angle$. I don't know that I've seen $\angle \mathbf{ab}$ before though.

Answer 2

You can also use the symbol $\measuredangle$.

Answer 3

I like the following method:

..., where $\theta$ is the angle between vectors $\vec{a}$ and $\vec{b}$...

Seriously, words can really improve proof legibility, and should be used.

Answer 4

The $\angle$ symbol is to represent an angle that is "fixed in space" - its position and orientation in space are fixed. Suppose you have points $A, O, B$ in space, you could talk about the angle $\angle AOB$.

However, your vectors $\vec{a}, \vec{b}$ seem to be direction vectors which are not anchored anywhere, and the angle you wish to denote is simply a real number value that is not "anchored" anywhere in space.

Unless you are treating $A = \vec{a}, B = \vec{b}$ and you are finding the angle they form with $O$ as the origin, you should either use mixedmath's answer or $\cos^{-1}(\hat{a} \cdot \hat{b})$ to denote the angle.

Answer 5

What's wrong with using the identity that $a\cdot b = |a||b|\cos{\theta}$ and solving for theta?