Year 12 Maths Extension 2 (2027)
Vectors
Cauchy–Schwarz Inequality
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Questions
Question 1
183488
State the Cauchy–Schwarz inequality for two vectors \(\mathbf{a}\) and \(\mathbf{b}\), and state the condition for equality.
\(|\mathbf{a}\cdot\mathbf{b}| \le |\mathbf{a}|\,|\mathbf{b}|\); equality if and only if \(\mathbf{a}\) and \(\mathbf{b}\) are parallel (one is a scalar multiple of the other).
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