In mathematics, a vector is a quantity that has both magnitude and direction. Vectors are typically represented as arrows or as ordered pairs or triplets of numbers that describe their components along different axes. They are utilized to represent physical quantities such as displacement, velocity, and force.

A scalar quantity has only magnitude (size), whereas a vector quantity possesses both magnitude and direction. For example, distance and speed are scalars, whereas displacement and velocity are vectors.

Collinear vectors are vectors that lie on the same straight line, or in other words, one vector is a scalar multiple of the other. For example, if , then and are collinear vectors.

Vectors are used to represent physical quantities that have both magnitude and direction. Examples include displacement, velocity, acceleration, and force. In physics, vectors are essential for analyzing motion, forces, and other directional quantities.

Vectors are a crucial topic in class 12 mathematics, providing the foundation for more advanced studies in physics, engineering, and higher mathematics. They are also a significant component of various competitive exams like IIT JEE, where vector algebra is often tested.