Arranging Unit Vectors How many unique orientations can three unit vectors be arranged, if all three unit vectors must be perpendicular? Here, a unique orientation is one that cannot be rotated by less than 90 degrees into another orientation. Each orientation can define a coordinate system, since each unit vector can point in the positive direction of an axis. Two coordinate systems related by less than a quarter of a rotation are considered equivalent in contrast to unique, to avoid counting a numerous amount of coordinate systems formed by rotations. Finally, which of the resulting orientations of unit vectors form …
