To rotate a vector x around another vector z, you can use the cross product formula: x' = x * cosθ + (z x x) * sinθ + z * (z · x) * (1 - cosθ), where x' is the rotated vector, θ is the angle of rotation, and · represents the dot product.
The purpose of rotating a vector around another vector is to change the direction of the vector while keeping its magnitude unchanged. This operation is commonly used in computer graphics, physics, and engineering applications.
Yes, you can rotate a vector around any arbitrary vector as long as the two vectors are not parallel. If the two vectors are parallel, the rotation will result in the same vector.
The direction of rotation affects the resulting vector by changing the sign of the angle of rotation. A positive angle of rotation will result in a counterclockwise rotation, while a negative angle will result in a clockwise rotation.
Yes, there is a difference between rotating a vector around a fixed point and rotating it around another vector. When rotating around a fixed point, the vector will rotate around that point in a circular motion. However, when rotating around another vector, the vector will rotate around an axis that is perpendicular to both the original and the rotating vectors.