Zero and Parallel Vectors in R^2
Consider vectors \(\mathbf{u} = (a, b)\) and \(\mathbf{v} = (2a, 2b)\) in \(\mathbb{R}^2\). (a) Explain why \(\mathbf{v}\) is parallel to \(\mathbf{u}\). (b) Discuss the special role of the zero vector in the context of vector parallelism.