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HOW CAN WE MULTIPLY TWO VECTORS ?
Multiplication of vectors:
(i) Multiplication of one vector by a second vector so as to produce a scalar. It is called scalar product or dot product of two vectors.
(ii) Multiplication of one vector by a second vector so as to produce another vector. It is called vector product or cross product of two vectors.
Scalar product of two vectors
Consider two vectors and with angle θ between them as shown in the figure. The scalar product of vectors and is defined as:
               
                                            
where A and B are the magnitudes of the vectors and θ is the angle between them when their tails touch. Since A, B and cos θ are scalars, the product (read "A dot B") is * also scalar. The equivalent definition of scalar product is as under:
The Scalar product of two vectors and is defined as product of magnitude of one vector (say A) and the scalar component of the other vector (B cos θ) along the direction of the first vector .
The vector or cross product of two vectors is defined as the vector whose magnitude is equal to the product of the magnitudes of two vectors and sine of the angle between them and whose direction is perpendicular to the plane of the two vectors and is given by right hand rule. Mathematically, if  θ is the angle between vectors and , then
           


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