What is the angle between A(2,3,4,1) and B(1,-2,-1,-1)?

Answer 1

You have described two points in four-dimensional hyperspace. Although angles can be defined in hyperspace, one needs to know the bases of such space.

For example, in three D space, I could write A(2,3,1) and B(1,-2,-1), but would be unable to do the angle because the bases are unspecified. It could be rho, theta, r or x, y, z for example. The first bases is the conventional spherical bases and the second is the standard Cartesian bases. Transformation of the coordinates can show they are equivalent.