# Oh, those are vector!

Algebra Level 4

$\sqrt{a^2+ab+2b^2}+\sqrt{b^2+bc+2c^2}+\sqrt{c^2+ac+2a^2}$

Given that $$a,b$$ and $$c$$ are real numbers satisfying $$a+b+c\geq1007$$, find the minimum value of the expression above.

Bonus: Try to solve this problem using vectors.

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