# What does this vector notation mean?

• I
Yealtas
Hello,

I'm currently doing vectors in class, but I don't know what these parts mean.

Especially φ(a,b). I understand cos(φ), but I don't understand cos(φ(a,b)). φ is the angle between two vectors a and b, but what does the (a,b) part add?

I tried to google, but I couldn't really find anything helpful. Again, I'm not interested in proof or anything of the likes right now. For now I am just trying to decipher the symbols so I understand what I am doing.

Thanks in advance for the help.

DoItForYourself
The (##\vec a, \vec b##) part just informs someone that the angle φ is the angle between the vectors a and b (without the obligation to write it in words) as you correctly said.

fresh_42
Mentor
Hello,

I'm currently doing vectors in class, but I don't know what these parts mean.

Especially φ(a,b). I understand cos(φ), but I don't understand cos(φ(a,b)). φ is the angle between two vectors a and b, but what does the (a,b) part add?
It is simply rigor. ##\varphi (\vec{a},\vec{b})## is what you wrote: angle ##\varphi ## between ##\vec{a}## and ##\vec{b}##. As the angle depends on the vectors, and the order, it is simply the precise way to write it, so ##\varphi = \varphi (\vec{a},\vec{b})##.
I tried to google, but I couldn't really find anything helpful. Again, I'm not interested in proof or anything of the likes right now. For now I am just trying to decipher the symbols so I understand what I am doing.

Thanks in advance for the help.
The other marked notation means: If ##\vec{a}=(a_1,\ldots ,a_n)## in coordinates, then for the length of the vector ##|\vec{a}|^2 = a_1^2+\ldots + a_n^2##. It's the theorem of Pythagoras.

Yealtas
The (##\vec a, \vec b##) part just informs someone that the angle φ is the angle between the vectors a and b (without the obligation to write it in words) as you correctly said.
It is simply rigor. ##\varphi (\vec{a},\vec{b})## is what you wrote: angle ##\varphi ## between ##\vec{a}## and ##\vec{b}##. As the angle depends on the vectors, and the order, it is simply the precise way to write it, so ##\varphi = \varphi (\vec{a},\vec{b})##.

The other marked notation means: If ##\vec{a}=(a_1,\ldots ,a_n)## in coordinates, then for the length of the vector ##|\vec{a}|^2 = a_1^2+\ldots + a_n^2##. It's the theorem of Pythagoras.
Thanks, both of you. :)