Normally, if we were to find the angle between two vectors, say **up-vector** and **dir-vector**, what we would do is to do a dot product between them. Since

and

However, since the calculated angle is the smallest / nearest angle between the two vectors, we can’t derive the (rotational) direction of one vector from the other. Thus in the following figure, it’s hard to figure out whether the **direction vector** is on the left or right of the **up vector**. The angle between two vectors calculated using dot product is always between 0° to 180°, thus we are not able to derive the direction from it. Continue reading