No, a scalar quantity cannot possess a direction.

Scalar quantities are physical measurements that are completely characterized by their magnitude (or numerical value) alone. Unlike vector quantities, scalar quantities do not have an associated direction. Examples of scalar quantities include time, temperature, speed, energy, mass, and volume. These quantities can be manipulated mathematically through addition, subtraction, multiplication, or division, similar to ordinary numbers, making them simpler to work with than vector quantities.

For instance, if you have $5$ apples and you add $3$ more, you now have $8$ apples. The count of apples is a scalar quantity since it only involves a magnitude (the number of apples) without any directional component. Similarly, if the temperature outside is $20$ degrees Celsius and it drops by $5$ degrees, it is now $15$ degrees Celsius. Again, this scenario involves only a magnitude, not a direction.

In contrast, vector quantities—such as force, velocity, and displacement—are defined by both a magnitude and a direction. For example, stating that a car is moving at $60$ km/h denotes speed, which is a scalar quantity. However, if you specify that the car is moving at $60$ km/h to the north, this describes its velocity, a vector quantity. The direction (to the north) is essential for fully understanding the car’s motion.

In physics, recognizing the distinction between scalar and vector quantities is crucial, as they behave differently. Scalar quantities adhere to the conventional laws of arithmetic, while vector quantities follow a different set of rules known as vector algebra. For example, when adding vector quantities, both their magnitudes and directions must be considered, which can complicate calculations.

In summary, scalar quantities are numerical representations of the magnitude of a physical quantity and do not include a directional component. This absence of direction is what differentiates them from vector quantities.