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

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

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.

• and/or a drawing can help – jk. Feb 5 '13 at 8:07

You can also use the symbol $\measuredangle$.

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

• I know that symbol. But it seems to be used in the occasion where an angle is made by three points or just to use an alphabet to represent an angle without indicating form of the angle. – ymfoi Feb 5 '13 at 3:14
• I think your symbol is used when you have a triangle ABC to say that ∠ABC is the angle formed by the intersection of sides A and C, but I do not think you can use if you talk about vectors – dwarandae Feb 5 '13 at 3:15

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.

You can explicitly denote it once, i.e. give it a variable name like $\theta_{ab}$. For example,

..., where $\theta_{ab}$ denotes the angle between vector $\vec{a}$ and $\vec{b}$.

From there on, you just write $\theta_{ab}$, and all should be clear.

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

• It's just a matter of notation, since we don't like to write the words "the angel between vector a and b" over and over again in our claims. – ymfoi Feb 5 '13 at 6:03