Scalars : A physical quantity which needs only magnitude, i.e. a number and a unit of measurement to specify its value is defined as a scalar. e.g. Mass of 2 kg, length of 20m, time interval of 5 sec etc. Thus mass, and length, time are scalars.
Vectors : A Physical quantity which needs magnitude and direction to specify its value is defined as a vector. e.g. Velocity of 285 km/hr along N-E direction, Momentum of 47 kg x m/s along 300 to East of south direction. Thus velocity and momentum are vectors.
Vector Algebra
As vectors have direction (besides magnitude) their sum or difference or multiplication cannot be done using the algebra of scalars. The algebra of vectors has to be developed from the following.
Addition of vectors
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Alternatively, the method called Parallelogram law of vector addition can also be used as shown in figure 2.
Physical quantities like work, flux are scalar quantities with which two vectors are expressed as scalar or dot products of two vectors. On the other hand quantities like angular momentum, force on a moving charge in a magnetic field are vectors with which two vectors are associated. They expressed as vector cross product of two vectors.
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