Scalar vs. Vector

Definition: Scalar quantity only has a magnitude information whereas vector quantity is defined by both a magnitude and a direction.

Key difference: directionality is the key trait of a vector, which is a property of many real world phenomenon.

Examples:

• Power is a scalar quantity. We can sum power loss of the circuit by adding up the the losses.
• Electromagnetic(EM) waves are vector quantity. Summing two incident EM waves at one point requires the information on amplitudes and relative phase information (effect of direction and path differences). Depending of phase differences (i.e arrival delay between two waves at incident point), the resultant amplitude lies between sum and difference between two amplitudes.