A Coefficient over a Norm

★ 7/10Extrema Completing the Square vectors

Problem

Let $\vec{e_1},\vec{e_2}$ be unit vectors with angle $\dfrac{\pi}6$ between them, and let $\vec b=x\vec{e_1}+y\vec{e_2}$ be a nonzero vector with $x,y\in\mathbb R$ . Find the maximum value of

\frac{|x|}{\left|\vec b\right|}.

Answer

Solution

Difficulty	7/10
Topics	Extrema, Completing the Square, vectors

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