Explain the kinds of multiplication operations for vectors .

Explanation

There are two kind of multiplication of vectors :
(i) If the product of two vector quantities results into a scalar then the product called a scalar product . This product is also known as dot product .
The scalar products of two vectors `vec(A) and vec(B)` is denoted by
`vec(A ) . vec(B ) = | vec(A) | |vec(B)|` where A and B are the magnitudes of `|vec (A)|and |vec (B)|` respectively and `theta` is the angle between `vec(A) and vec(B)`
(ii) Vector product [Corss product ] :
If the product of two vector quantities results into a vector then the product is called a vector product .
A vector product is represente d by keeping cross sign `(xx)` between two vectors hence it is also called cross product of vectors .
Suppose `theta ` is the angle between `vec(A) and vec(B)` then its vector product is ,
`vec(A).vec(B ) = |vec(A) ||vec(B)|sin theta hat (n)`
`= AB sin theta hat(n)` where `hat(n)` is the unit vector in the direction perpendicular to the plane formed by `hat(A) and hat(B)` and B are the magnitude of `hat(A) and hat(B)` respectively .