Three Dot Products, One Norm

Problem

Plane vectors $\vec a, \vec b, \vec c$ satisfy

\vec a \cdot \vec b = 1, \qquad \vec b \cdot \vec c = 1, \qquad \vec c \cdot \vec a = 2.

Find the range of $\left|\vec a + \vec b + \vec c\right|$ .

Answer

Solution

Difficulty	7/10
Topics	inequality, vectors

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