vectorrotation
Vector rotation is a fundamental operation in geometry and linear algebra that involves changing the orientation of a vector without altering its magnitude. Imagine a vector as an arrow originating from a point; rotating it means spinning that arrow around a fixed point, typically the origin, by a specified angle.
In two-dimensional space, a vector (x, y) can be rotated counterclockwise by an angle θ around the
[ x' ] = [ cos(θ) -sin(θ) ] [ x ]
[ y' ] [ sin(θ) cos(θ) ] [ y ]
In three-dimensional space, rotation is more complex as it requires specifying an axis of rotation in addition
Vector rotation is crucial in various fields, including computer graphics for orienting objects, robotics for controlling