Scalars & Vectors

Definition of Scalars and Vectors

Quantities in physics can be classified as scalars or vectors depending on whether they have direction as well as size.

• Scalars have magnitude only. This means they are described by a number and a unit, but no direction.
• Vectors have both magnitude and direction. They require a number, unit, and a direction to be fully described.

Examples of scalars include:

• Speed (e.g. 30 m/s)
• Mass (e.g. 5 kg)
• Temperature (e.g. 20 6C)

Examples of vectors include:

• Force (e.g. 10 N to the right)
• Velocity (e.g. 15 m/s north)
• Displacement (e.g. 5 m east)

For example, a displacement of 3 m east is represented by a vector arrow 3 cm long pointing east (scale 1 cm = 1 m).

Representing Vectors

Vectors are represented graphically by arrows:

• The length of the arrow shows the magnitude (size) of the vector.
• The direction of the arrow shows the vector6s direction.

These are called vector diagrams. They help visualise vectors and how they combine.

When adding vectors graphically:

• Place the tail of the second vector at the head of the first vector.
• The resultant vector is drawn from the tail of the first vector to the head of the last vector.

For example, if a person walks 3 m east then 4 m north, the resultant displacement vector points from the start to the final position.

The length of the resultant arrow can be measured and scaled to find the magnitude, and the angle measured to find the direction.

Scalar and Vector Quantities in Forces

Forces are vector quantities. This means they have both magnitude (size) and direction.

This is important because the effect of a force depends on its direction as well as its size. Two forces of the same magnitude can have very different effects if they act in different directions.

In contrast, scalar quantities related to forces, such as the magnitude of force alone, do not include direction.

When calculating forces, the direction must always be considered to understand the overall effect on an object.

For example, a 10 N force pushing a box to the right will move it differently than a 10 N force pushing it to the left.

This is why forces are represented as vectors in diagrams and calculations.

See the topics Forces as Vectors and Resultant Forces for more on how forces combine and act on objects.