A scalar is a quantity that is described by a single number – its magnitude. It does not have a direction.
📐 Example: The temperature of a room is 22 °C. The number 22 is enough to describe the temperature – no direction is needed.
A vector is a quantity that has both a magnitude and a direction. It is usually represented by an arrow.
🚗 Example: A car travels 60 km/h to the north. The speed 60 km/h is the magnitude, and “to the north” is the direction.
Imagine you’re planning a road trip.
Tip 1: When a problem asks for a magnitude only, you’re dealing with a scalar. If it asks for a magnitude and direction, it’s a vector.
Tip 2: Always check the units. Scalars often have units like J, kg, s, while vectors have directional units (e.g., m/s with a direction).
Tip 3: Remember that adding vectors requires both magnitude and direction. Scalars can be added simply by summing the numbers.
📝 Practice: Write down the vector components for a force of 10 N at 30° above the horizontal. Then calculate its horizontal and vertical components.
| Type | Examples | Key Feature |
|---|---|---|
| Scalar | \$v\$, \$T\$, \$m\$, \$E\$, \$t\$, \$q\$ | Only magnitude |
| Vector | \$\mathbf{v}\$, \$\mathbf{a}\$, \$\mathbf{F}\$, \$\mathbf{s}\$, \$\mathbf{p}\$, \$\mathbf{E}\$ | Magnitude & direction |