The conversation between human and AI assistant.
How can I prove that (A × B) − (C × D) = (A − C) × B ∪ A × (B − D)?
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Now, by the distributive property of vectors, we have (A − C) × B = A × B − C × B, which we can substitute into the right side of the equation to get (A − C) × B ∪ A × (B − D) = (A − C) × B ∪ A × B − A × D.