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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