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 points in the direction. Vectors are used in various fields, including physics and engineering, to describe quantities such as force, velocity, and displacement. In a coordinate system, vectors can be expressed using components, typically in the form of x, y for two-dimensional space. This allows for easier calculations and analysis of their properties. Understanding vectors is essential for solving problems related to motion and forces in both theoretical and practical applications.