# Vector of Steepest Ascent

Geometry Level pending

A three dimensional vector is given by $$V =(1, 3, 2)$$. We want to find the unit vector $$U$$ that is orthogonal to $$V$$ and has the maximum ascent, that is, the maximum $$z-$$component. If $$U = (a, b, c)$$ then find $$\lfloor 1000(a+b+c) \rfloor$$.

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