Chapter 6.3, Problem 19E

Let u₁ = $\left[\begin{array}{c}1\\ 1\\ -2\end{array}\right]$, u₂ = $\left[\begin{array}{c}5\\ -1\\ 2\end{array}\right]$, and u₃ = $\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]$.Note that u₁ and u₂ are orthogonal but that u₃ is not orthogonal to u₃ or u₂. It can be shown that u₃ is not in the subspace W spanned by u₁ and u₂. Use this fact to construct a nonzero vector v in ℝ³ that is orthogonal to u₁ and u₂.