A Vector-Locked Triangle

★ 8/10trigonometry Law of Cosines Completing the Square Triangle Geometry vectors

Problem

In $\triangle ABC$ , the sides opposite $A, B, C$ are $a, b, c$ , and

\left|\overrightarrow{BA} + \overrightarrow{BC}\right| = 2, \qquad \overrightarrow{AB}\cdot\overrightarrow{AC} = 2.

Find the minimum value of $b^2 - ab$ .

Answer

Solution

Difficulty	8/10
Topics	trigonometry, Law of Cosines, Completing the Square, Triangle Geometry, vectors

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