Does the following implication always hold?
$$\bf{a\times c=b \times c} \implies a=b$$
2026-03-29 12:12:12.1774786332
Does same cross product imply equality of two vector?
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$$ a\times c = b\times c \;\; \Longrightarrow \;\; (a-b)\times c = 0 \;\; \Longrightarrow \;\; c=0 \;\lor\;\exists \lambda : a-b = \lambda c $$ All we can say is that either $c=0$ or the difference of $a$ and $b$ is collinear with $c$.