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Scalar and Vector: Introduction and Concept

Physics is a based on mathematics, it is a mathematical science. The underlying principles and concepts of this subject have a mathematical basis. Throughout the entire course of our study of physics, we will face a variety of problems and concepts that have mathematical basis associated with them. Humans invented math and science to describe and understand the world around us. We live in at least four-dimensional world governed by time and three space dimensions namely up-down, left-right, and back-forth. The motion of objects can be easily described by words even by a layman who does not have enough knowledge in physics just by using a collection of words such as speeding up, slowing down, going fast, stopped, and turning etc. These words provide a sufficient vocabulary for describing the motion of objects. In physics we will be using vocabulary with words such as displacement, distance, speed, velocity, and acceleration etc. As we will observe soon that these words are associated with mathematical quantities and have strict definitions. In our daily life we observe that there are some quantities and processes which depend on the direction, and there are some quantities which do not depend on direction. The mathematical quantities that can be used to describe the motion of objects in our daily life can be divided into two categories. The quantity is either a scalar or a vector quantity. These two categories can be differentiated from one another by their definition:

Scalars quantities: Described by a magnitude or numerical value alone.

Vectors quantities: Described by both magnitude as well as direction.

Most of the physical quantities that are used in physics are either scalar or vector quantities. A scalar quantity is one which has magnitude only. For example time, length, speed, volume, temperature etc. A scalar quantity or parameter has only magnitude no directional component. Like the units for time are seconds, minutes, days, hours, etc represent an amount of time only and signifies nothing of direction. More examples of scalar quantities are mass, density and energy etc. Scalars quantities are represented by a single letter, usually small such as a. A vector quantity is that quantity which has both magnitude and direction. e.g. velocity. Vector quantities are represented by a single letter in bold type and with an arrow above the letter,

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