I don't understand why the Y component represent the angle between two vectors

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#1

I’ve been trying to make my arms pointing directly at my mouse but i can’t seem to figure it out so i decided to go to the forum and look for solution. Well, i came across this formula of CleverSource (Need help with torso and head following mouse - #7 by CleverSource) . It is not actually what i wanted because CleverSource makes this to rotate the head and torso instead of arms but it is still usable. The question that i want to ask is related to math. As you can see, this line

(((HeadPosition - Point).Unit):Cross(TorsoLookVector)).Y * 1

is to calculate the yaw axis to rotate head and torso.but it doesn’t make much sense to me. How can the cross vector Y component relative to the angle to rotate along the yaw axis? I’m kind of really tired due to homeworks, exams as well as lost orientation in scripting mainly due to the fact that i don’t know what goal that i can achieve for the last few weeks so if anyone can help? It would be so meaningful to me

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Need mathematical explanation
#2

I don’t believe it represents any kind of actual angle, but using the Y component to set the angle will make it move some arbitrary amount as the body rotates

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#3

(I am still learning this stuff too, so it may be all wrong)

The Y vector is the vertical axis right? When you start boiling the 3 dimensions down into their components, one of the questions is “how much do I turn left and right?” That’s spinning the vertical axis.

Obviously, that’s not the whole story. You want to look up and down too. But simplified, it’s just Y.

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#4

Can you explain it more specific, pls?

#5

yeah but how does it relate to angle? The y component magnitude is equal to the angle and why?