I am without hope. The cross product could save me.
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If I could wield the cross product. How would I know the new arrow points the right way?
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I could draw a picture of the desired cross product. But it would not be the real object. And I could pick a first vector - any vector which is orthogonal, and strong, and a real object - and sketch the second, and seek out that object.
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What if there were an operator × where i × k = j, and k × i were h instead of -j?
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End of conversation
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