What is a Vector?

A scalar is a size only: a mass of 3 kg, a time of 4 s, a temperature of 20 °C, a distance of 100 m. A vector has a size and a direction.

Physics starts with two vectors. A force is a push or a pull, measured in newtons (N): a push of 50 N to the right. A displacement is how far and which way something moved: 4 m east.

Two vectors: a push of 50 N to the right, and a move of 4 m east.

A vector is drawn as an arrow. Its length shows the size, called the magnitude, and the arrow points in its direction.

Along a straight line, a sign is enough to show the direction. Choose one direction as positive, east here, so a displacement d = +4 m is 4 m east and d = -3 m is 3 m west.

The sign is only the direction. A displacement of -3 m is not less than nothing: its magnitude is 3 m, the other way. A distance has no sign: walking 3 m west is a distance of 3 m.