Determining Regions via Dot Product Conditions
Let \(\mathbf{a} = (a_1, a_2)\) be a fixed nonzero vector in \(\mathbb{R}^2\) and \(\mathbf{x} = (x_1, x_2)\) be any vector. Consider the set \(R = \{ \mathbf{x} \in \mathbb{R}^2 : \mathbf{a} \cdot \mathbf{x} \ge 0 \}\). Explain geometrically the nature of the region \(R\) in the plane. In your answer, describe the boundary of \(R\) […]