g_edgar said:in general (not orthogonal, not unit length) you might say that A,B,C in that order is right-handed iff the triple scalar product (A x B) . C is positive.
A right-handed system is a three-dimensional coordinate system where the positive direction of the x-axis is to the right, the positive direction of the y-axis is upwards, and the positive direction of the z-axis is towards the viewer.
In a right-handed system, the direction of the cross product (AxB) is determined by the right-hand rule, where the thumb points in the direction of the cross product when the fingers of the right hand curl in the direction of A and then towards B.
This notation represents the cross product between two vectors, A and B, in a right-handed coordinate system. The resulting vector, C, is perpendicular to both A and B and follows the right-hand rule for direction.
Yes, it is possible to convert a right-handed system to a left-handed system by reversing the direction of one of the axes. However, this may result in changes to the mathematical representations and rules in that system.
A right-handed system is commonly used in applications involving geometry, physics, and computer graphics. It is also often used in engineering and navigation for its consistent and intuitive representation of space.