ABSTRACT
The concept of a scalar is easy to grasp as a quantity that has a particular value, such as the kinetic energy of an object, the air pressure at sea level, or the temperature in students oven. The concept of a vector is also relatively straightforward, generally being presented as a directional quantity that has magnitude as well as direction. The concepts of scalars and vectors come with some basic arithmetic rules. Scalar quantities may be multiplied together, resulting in a new scalar quantity of a different physical dimension, or added, resulting in a new scalar quantity of the same dimension. Scalars are just numbers and their values, unlike the vector components, are the same regardless of the choice of basis. Vector fields with scalar potentials are typically encountered at very early stages of physics education although it will generally not be stated in the language of vector analysis.
