Some physical quantities are completely described by a numerical value alone. Such quantities are called scalars or scalar quantity.
But for description of some physical quantities value as well as direction is required. Velocity of a particle is one such example. The magnitude of velocity is represented by a number such as 5 m/s and tells us how fast a body is moving. But description of velocity is complete only when direction of velocity is specified. Such quantities are called vectors.
Equality Of Vectors
Two vectors are equal if and only if they have same magnitude(numerical value) and direction. Thus, a parallel translation of a vector does not bring about any change in it.
Addition Of Vectors
Vectors cannot be added subtracted by normal laws of algebra. they are added according to The triangle law of vector addition. The parallelogram law of vector addition and The polygon law of vector addition are extensions of triangle law.