How to check if vectors are facing same direction

Question

I am working on a question where I am working within a right-handed coordinate system where the y-axis is straight up. I am supplied a structure that represents a 3-dimensional vector that looks like this:

struct vec{float x; float y; float z; };

I need to write a function that takes in a unit vector representing north and a unit vector represent a player's forward vector, and return if they are facing more north than south. Unfortunatly I have no idea where to go from here, I believe I have to do something like:

PlayerDirection = sqrt((PlayerVector.x *= PlayerVector.x)
                     + (PlayerVector.y *= PlayerVector.y)
                     + (PlayerVector.z *= PlayerVector.z));

But I do not know where to go from here. Any help/explanation would help, thanks.

Answer 1

apply a dot product to both vectors. The dot product will be positive if the angle between both vectors is smaller than 90 degrees, and negative otherwise.