Scalars, vectors, and adding vectors

A scalar quantity has only a size (magnitude), like distance, speed, mass, or time. A vector quantity has both a magnitude and a direction, like displacement, velocity, acceleration, or force. Vectors are drawn as arrows and added head to tail: the resultant is the arrow from the tail of the first to the head of the last. When two vectors are perpendicular, the Pythagorean theorem gives the resultant's size: walking 3 meters east and then 4 meters north gives a displacement of 5 meters (to the northeast), even though the distance walked is 7 meters. Breaking a vector into perpendicular components works the same way in reverse, and is how two-dimensional motion is analyzed.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report