Hey guys I am a beginner in linear algebra. I am doing vectors now and I just noticed that when two vectors are parallel (or antiparallel), the product of their norms is equal to the absolute value of their dot product, or(adsbygoogle = window.adsbygoogle || []).push({});

[tex] |u \cdot v | = ||u|| \ ||v|| [/tex]

I know that this is a special case of the Cauchy-Schwarz inequality. My question is, is the converse necessarily true? In other words, if you know the above equation to be true for a pair of vectors u and v, must they necessarily be parallel? How might one go about proving this? Could we assume the contrary and show an inconsistency?

By the way, by parallel, I mean to say that two vectors are parallel if there exists a scalar (real number, not necessarily positive) that scales one vector onto the other.

BiP

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# Dot product = Product of norms

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