Question: Find a vector field (mathbf{F}) in the plane such that (|mathbf{F}(x, y)|=1) and (mathbf{F}(x, y)) is orthogonal to (mathbf{G}(x, y)=langle x, yangle) for all (x,

Find a vector field $\mathbf{F}$ in the plane such that $\|\mathbf{F}(x, y)\|=1$ and $\mathbf{F}(x, y)$ is orthogonal to $\mathbf{G}(x, y)=\langle x, yangle$ for all $x, y$.

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