MathCastle
TrigonometrySuperchallenge

Trigonometry · Superchallenge problem

Vectors a\mathbf a, b\mathbf b, c\mathbf c satisfy a+b+c=0\mathbf a + \mathbf b + \mathbf c = \mathbf 0, with ∣a∣=3|\mathbf a| = 3, ∣b∣=4|\mathbf b| = 4, and ∣c∣=5|\mathbf c| = 5. Find a⋅b+b⋅c+c⋅a\mathbf a\cdot\mathbf b + \mathbf b\cdot\mathbf c + \mathbf c\cdot\mathbf a.

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