What is a Vector?

A scalar is a size only: a mass of $3\ \mathrm{kg}$, a time of $4\ \mathrm{s}$, a temperature of 20 °C, a distance of $100\ \mathrm{m}$. 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 $50\ \mathrm{N}$ to the right. A displacement is how far and which way something moved: $4\ \mathrm{m}$ east.

Two vectors: a push of $50\ \mathrm{N}$ to the right, and a move of $4\ \mathrm{m}$ 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 $d = +4\ \mathrm{m}$ is $4\ \mathrm{m}$ east and $d = -3\ \mathrm{m}$ is $3\ \mathrm{m}$ west.

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