If you have a question you should ask a question and not posting an answer.

Sorry but your question doesn’t really make much sense. What do you mean by " 45° relative to the plane"? Note that “rotated vector” could mean anything. What is your starting vector and around which axis do you actually rotate? Do you apply euler angles rotation? What is even your plane normal? You can’t get (0, 0.71, 0) when you have a normal that points in the world up direction (0,1,0). That means you clearly use a different plane / plane normal.

Whatever you tried to ask here doesn’t seem to be related to the **question that has been asked here** since you have different vectors. Please don’'t try to hijack the question of someone else. Answers which are posted to a question have to answer the question that was asked here. If you have a similar question but this one doesn’t fully answer your specific case, ask a seperate question.

## However

If you do ask a question make sure you include all necessary information to understand your case. If you have a vector tell us it’s initial state. If you apply rotations to it, tell us around which axis.

Anyways i try to give a best guess answer here. However if it doesn’t clear up your confusion, please ask a seperate question.:

Since in your second example the z component of your vector is 0 we can assume your plane normal is most likely either forward or -forward (0,0,1). So after a projection only the x and y components remains. Lets assume further that your initial vector you’re going to rotate is (0,1,0). In your first case you most likely applied a rotation around the x axis. Sin(45°) as well as Cos(45°) are both 0.707 (actually 1/Sqrt(2) or Sqrt(0.5)). So when rotating (0,1,0) around x(1,0,0) by 45° we get (0, 0.707, 0.707). Projecting down we just drop the z component and get (0, 0.707, 0).

However now before we project down we further rotate our (0, 0.707, 0.707).vector around y (0,1,0) also be 45° This will lead to (0.5, 0.707, 0.5) To check we can calculate the length of this vector and it is still 1. It’s just Sqrt(0.5² + 0.707² + 0.5²) == Sqrt(0.25 + 0.5 + 0.25) == Sqrt(1) == 1.

Of course when you project down that vector (again just dropping the z component) we get (0.5, 0.707, 0). Though i’m not quite sure what’s unintuitive about that result.