Scalar Multiplication

A recipe calls for 3 cups flour and 2 cups milk — a vector (3, 2) of ingredients. To double it you multiply everything by 2: (6, 4). The ratio stays identical, the direction of the recipe unchanged, only the scale grows. Multiply by ½ and you shrink it; multiply by −1 and you reverse it entirely. This is scalar multiplication — resizing a vector without bending its line.