Explanation

Vectors have both magnitude (size) and direction. Written as column vectors (3, 4) or with arrow notation. Scalars have only magnitude (regular numbers). Velocity is a vector; speed is scalar.

Addition: add corresponding components. (2, 3) + (4, 1) = (6, 4). Graphically, place vectors head-to-tail. Subtraction: add the negative. Scalar multiplication multiplies each component.

Magnitude: √(x² + y²). Direction: arctan(y/x). Applications: physics (force, velocity), navigation, computer graphics. Vectors describe quantities where direction matters.