I'm having trouble understanding the concept. A quarter rotation simply means rotation of 90 degrees right? It doesn't indicate the direction it rotates to. But cross product has a specific direction.

Are there any other ways to represent rotations in graphics?

Can we use the rotation matrix to get a rotation by arbitrary angle?

u and (N x u) form an orthogonal (not necessarily normal) basis for the plane, so I believe to achieve an arbitrary rotation theta, we can take cos(theta) times u, and sin(theta) times (N x u)

The wording “quarter rotation in the plane with normal N” suggests that the vector nxu is a quarter rotation from the vector u specifically. Isn’t the vector nxu a quarter rotation, or 90 degrees, away from both n and u?

We can take additional cos(theta) to make it?

I think cos(theta)u + sin(theta)(N x u) would do the trick?

Is this the most common way to perform rotations on vectors and objects in computer graphics or are there other methods that are more commonly used or efficient?

Is there a simple intuition for cross products in higher dimensions?