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 



