Does $A\wedge B=A\wedge C$ imply that $B=C$?
I need help figuring this out because I am lost on this
2026-03-26 21:25:23.1774560323
How to properly do wedges
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You asked "If A wedges B and A wedges C ...". Usually, a statement of the form "If X and Y" only makes sense if X and Y are things that can be true or false, hence our confusion. However, if we interpret it as "If $A \wedge B = A \wedge C$, does $B = C$?" - in other words, if the exterior vector products are equal are the vectors themselves equal?
The answer is no. If $A \wedge B = A \wedge C$, then it is satisfied in general if the vectors $A$ and $B - C$ are parallel, or the vector $A = 0$.