Scalar: The quantities which are represented by magnitude and no directions and follow the ordinary algebra are called scalar quantity. Example: mass, volume, speed, density etc.
Vector: The quantities which are represented by magnitude and directions and follow a special type of algebra (vector algebra) are called vector quantity. Example: velocity, acceleration, force etc.
Representation of a vector: A vector can be represented by joining two points with an arrow. 
represents a vector where point A is the initial point or origin and point B represents the terminal point. Arrow is directed from origin to terminal point. Let us consider,  is 
 and the magnitude of 
 is || = || = P = AB.
Classification of vector:
(i) Equal vector: If two vectors have equal magnitude and same direction then those vectors are called equal vector. Here (= ) and 
(= 
) are of same magnitude and same direction. So, = .
(ii) Opposite vectors: If two vectors have equal magnitude but opposite direction then those vectors are called opposite vector. Here (= ) and (= – ) have equal magnitude but opposite direction then = – .
(iii) Collinear vectors: If all the vectors are parallel to each other whatever be their magnitude then those vectors are collinear vectors. Here , Â and 
 are parallel so they are collinear vectors.
(iv) Null vector: The vector which having magnitude zero and the direction is undefined then the vector is called null vector.
(v) Orthogonal vector: Two vectors are said to be orthogonal if they are perpendicular to each other.
(vi) Unit vector: The vector which having magnitude one and the direction is towards the given vector is called unit vector. If is a vector then the unit vector 
= 
.
If = x
+ y
+ z
then the unit vector 
= 
 (where , and are the unit vectors along X, Y, Z axis respectively.)
