[Steps Shown] Find a vector in C^3 orthogonal to (1, 1, 1) and (1,ω ,omega ^2), where w=e^2pi
Question: Find a vector in \({{C}^{3}}\) orthogonal to (1, 1, 1) and \(\left( 1,\omega ,{{\omega }^{2}} \right)\), where \(w={{e}^{2\pi i/3}}\).
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