Vector
Definition
A quantity that has both a size and a direction — like velocity (60 km/h north) or force (pushing east). Vectors are the language of motion in physics.
Technical definition
A mathematical object with magnitude and direction, typically represented as an arrow or an ordered tuple of components. Vectors add tip-to-tail and follow the parallelogram rule; in coordinates, a vector is specified by its components along basis axes.
Example
Walking 3 km east then 4 km north leaves you 5 km from home — not 7 km — because displacements add as vectors. The straight-line result comes from the Pythagorean theorem on the two legs.
Students often treat every quantity as a plain number. But adding two velocities pointing different ways is not simple addition — direction matters. Speed (60 km/h) is a scalar; velocity (60 km/h north) is a vector, and mixing them up breaks problems.