If a·b = c·b for all vectors b, show that a = c

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You guys have confused the living **** out of me, so I don't even know what the OP is going through. Besides set a good example. Let's be civilized.
 
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And what was the "intended meaning"...?I think it's a matter of subjectivity in this case,which has nothing to do with mathematics.

I'll drop it.

Daniel.