A vector is a mathematical object that has both magnitude and direction. It is often represented as an arrow, where the length of the arrow indicates the magnitude and the arrowhead shows the direction. Vectors are used in various fields, including physics and engineering, to describe quantities like force, velocity, and displacement. In a coordinate system, vectors can be expressed using components, such as x and y coordinates in two dimensions. This allows for easy calculations and visualizations of how vectors interact with one another. Understanding vectors is essential for analyzing motion and forces in real-world scenarios.