When a function takes vectors and applies a dot product, how do we know if the vectors need to be normalized to magnitudes of 1 first?

Question

Since normalisation takes a role here is there a syntax to state if the vector must be normalised first?

I am basically trying to convert this equation into computer code:

I am not particularly familiar with the origins of the function, but am not sure if i need to normalise my vectors for the dot product first. It doesn't say one way or another. So how are you generally suppose to know when you come across a new function like this?

Is there a syntax that implies the "normalized version of a given vector" because if not, how do you know what is the right intepretation ?

Answer 1

That "hat" on top of the $\hat{k}$ and on top of $\hat{w}$ is a notation that means a unit vector, so unless there is some "contract" that says your function will only be supplied with normalized vectors, you do need to normalize.