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.
Zero Vector Identification and Notation
Define the zero vector in Euclidean space and state its standard notation.