The Cauchy-Schwarz Inequality |u · v| ¤ ||u|| ||v|| is equivalent to the inequality we get by

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The Cauchy-Schwarz Inequality |u · v| ‰¤ ||u|| ||v|| is equivalent to the inequality we get by squaring both sides: (u · v)2 ‰¤ ||u||2 ||v||2
(a)
The Cauchy-Schwarz Inequality |u · v| ‰¤ ||u|| ||v|| is

Prove this algebraically.
(b) Prove the analogue of (a) in IR3.

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