I recently studied Fleming's Right Hand Rule and Fleming's Right Hand Rule for electromagnetism (For locating direction of Force, Magnetic Field and Current). Using my hands to find the direction is very tedious. Is it possible to use these rules by using vectors? If yes, how? I searched in Google for this but could not get a satisfactory answer. Please help.

I recently studied Fleming's Left Hand Rule and Fleming's Right Hand Rule for electromagnetism (For locating direction of Force, Magnetic Field and Current). Using my hands to find the direction is very tedious. Is it possible to use these rules by using vectors? If yes, how? I searched in Google for this but could not get a satisfactory answer. Please help.