A Sum of Two Norms

★ 6/10Extrema Cauchy-Schwarz inequality vectors

Problem

Vectors $\vec a, \vec b$ satisfy

\left|\vec a + \vec b\right| + 2\left|\vec a - \vec b\right| = 15, \qquad |\vec a| = 3.

Find the maximum and minimum values of $|\vec b|$ .

Answer

Solution

Difficulty	6/10
Topics	Extrema, Cauchy-Schwarz, inequality, vectors

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