Discuss why an infinitesimal displacement is regarded as a vector quantity.

Hint: Vector, in physics is a quantity that has both magnitude and direction.Infinitesimal rotations can be thought of as vector quantities since the body's description in a short period of time is more or less a straight line, which can be represented as a vector.

Complete answer:
Scalars and vectors are the two types of physical quantities that can be classed. Only numerical values and proper units can be used to express quantities like mass and density. Scalars are the name for these quantities. Quantities like velocity and force, on the other hand, necessitate the determination of a numerical value and a direction.

Specifying the value of velocity, for example, is insufficient to comprehend an object's motion. It's important to identify the direction in which it's moving. Vectors are the names given to such quantities.A quantity that is closer to zero than any normal real number but is not zero is called an infinitesimal or infinitesimal number.

A virtual displacement (or infinitesimal displacement) illustrates how the mechanical system's trajectory can hypothetically (thus the word virtual) diverge very slightly from the system's real trajectory without violating the system's limitations. Infinitesimal rotations are vector quantities because the body in a short period of time is more or less a straight line, which can be represented as a vector.

Note: It obeys the law of parallelogram of vectors which is a sufficient and necessary requirement for being a vector quantity. The law of commutation is immediately satisfied if this condition is met. So an infinitesimal displacement is regarded as a vector quantity.