In the book Field and Wave Electromagnetics by David K. Chen, I am asked whether the distributive law holds for cross product or not. However, I am asked not to resolve the vectors in Cartesian components and I also want to avoid the geometric approach( I found one and understood it). Is it possible to somehow prove the distributive law for cross product without geometric means or use of Cartesian coordinates? I am really confused by this, and I would be glad if you reply if it is not possible. Thanks in advance.