Explain vector with the help of examples

A change of position of a particle is called displacement. If a particle moves from a position A to a position B, as shown in the figure. We can represent its displacement by drawing a line from A to B. The direction of displacement can be shown by putting an arrowhead at B indicating that the displacement was from A to B, the path of the particle need not necessarily be a straight line from A to B; the arrow represents only the net effect of the motion, not the actual motion. Further more, a displacement such A’B’, which is parallel to AB, represents the same change in position as AB. We make no distinction between these two displacements. A displacement is therefore, characterized by a length and a direction.

Quantities that behave like displacements are called vectors. The word ‘vector’ comes from Latin and means ‘carrier’. Vectors then, are quantities that have both magnitude and direction and combine according to certain rules of addition. The displacement vector can be considered as the prototype. Some other physical quantities which are vectors, are force, velocity, acceleration, electric field strength and magnetic induction. Many of the laws of Physics can be expressed in a compact form using vectors; derivations involving these laws are often greatly simplified if this is done.

Quantities that can be completely specified by a number and unit and therefore, have magnitude only, are called scalars. Some scalar quantities are mass, length, time, density, energy and temperature. Scalars can be manipulated by the rules of algebra.