Multiplication of two vectors



Multiplication of two vectors
There are two types of the multiplication of two vectors:
 Scalar Product OR Dot Product
 Vector Product OR Cross Product
SCALAR PRODUCT
OR
DOT PRODUCT
Type of multiplication of two vectors in which the product is a scalar quantity is referred to as “Scalar Product OR Dot Product”
MATHEMATICAL REPRESENTATION OF SCALAR PRODUCT
Consider two vectors  and  making an angle q with each other. Their scalar product or dot product is defined as:
Scalar product of two vectors  and  is a scalar quantity which is equal to the
product of the magnitudes of 
 and  and the cosine of the angle between them.
  
EXPLANATION
EXAMPLE # 01
When we multiply two vector quantities force and displacement we get work which is a scalar quantity. Therefore, we can say that work is the scalar product or dot product of force and displacement.
 
EXAMPLE # 02
When we multiply two vector quantities electric intensity and normal area we get electric flux which is a scalar quantity. Therefore, we can say that electric flux is the scalar product or dot product of electric intensity and normal area