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What do I expect of -A?
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I expect that if I add -A to A,
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I should get the guy who plays the role of 0 in this world,
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which is the vector of no length.
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It's very clear that if you want to take A and ask,
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"What should I add to A so I get the null vector?"
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it's clear that you want to add a vector that looks like that,
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because then you go from the start of this to the finish of that,
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you end up at the same point
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and you get this invisible 0 vector.
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So the minus vector is the same vector flipped over,
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pointing the opposite way.