The definition u v = |u| |v| cos implies that |u v| |u||v|
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The definition u • v = |u| |v| cos θ implies that |u • v| ≤ |u||v| (because |cos θ| ≤ 1). This inequality, known as the Cauchy–Schwarz Inequality, holds in any number of dimensions and has many consequences.
Use the vectors u = (√a, √9) and v = (√b, √a) to show that √ab ≤ (a + b)/2, where a ≥ 0 and b ≥ 0.
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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