Undergrad What does this vector notation mean?

[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]

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. :)