Vector Ratio

Algebra Level 3

In the \(xyz\)-plane above, let \(O=(0,0,0)\) be the point of origin, \(P=(a,b,c)\), and \(Q=(a+b, b+c, c+a)\), where \(a,b,c\) are non-zero real numbers.

What is the maximum value of the ratio \(\frac{OQ}{OP}?\)

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