A vector is a quantity with both magnitude and direction, represented geometrically as an arrow.
Vectors are written as v = โจx, yโฉ in 2D or v = โจx, y, zโฉ in 3D. Vector operations include addition, subtraction, scalar multiplication, dot product, and cross product. Vectors describe displacement, velocity, force, and acceleration in physics.
Vector concepts emerged in the 19th century. William Rowan Hamilton developed quaternions (1843). Josiah Willard Gibbs and Oliver Heaviside independently developed modern vector analysis around 1880.