Vectors

A weather report says 'wind at 20 mph.' To fly a plane, you need more: 20 mph blowing FROM the southeast. The speed alone is a scalar; the speed-plus-direction is a VECTOR. Vectors are the language of anything that points: forces, velocities, displacements, magnetic fields. They have a magnitude (how big) and a direction (which way), and they add tip-to-tail and multiply in two distinct ways — the dot product (measuring alignment) and the cross product (measuring perpendicular area).