Scalar quantities

1. The magnitude of a quantity is its size, or numerical value.
2. A scalar has no associated direction, because its value on its own describes it fully.
3. Examples of scalars include mass ($5kg$), time ($20s$), temperature ($18{}^{\circ }C$), speed ($12m/s$), distance and energy.
4. Each is complete without a direction: it would be meaningless to describe a mass as “north” or a temperature as “to the left”.

Vector quantities

1. The direction matters: two vectors with the same magnitude but different directions are different vectors.
2. A force of $10N$ to the right is not the same as a force of $10N$ to the left.
3. Examples of vectors include force, velocity, acceleration, displacement, momentum and weight.
4. A complete description gives both magnitude and direction: “a force of $15N$” gives only the magnitude, but “a force of $15N$ upwards” gives both.

Representing vectors with arrows

1. A vector can be represented by an arrow drawn to a chosen scale.
2. The length of the arrow represents the magnitude of the vector.
3. The direction the arrow points represents the direction of the vector, and the arrowhead shows which way it acts.
4. A longer arrow represents a greater magnitude, provided the same scale is used throughout.
5. For example, a force to the right is drawn as a horizontal arrow pointing right; a larger force in the same direction is a longer arrow pointing right.

Describing a vector fully

1. To describe how an arrow represents a vector, give both marking points: the length shows the magnitude, and the arrowhead shows the direction.
2. To describe a vector itself, always state both its magnitude and its direction; a value and unit alone may not score full marks.
3. This is why $10N$ east and $10N$ west are different vectors: they have equal magnitude but opposite direction.