Vector Product

Vector product OR cross product
Type of multiplication of two vectors in which the product is also a vector quantity is referred to as “vector product OR cross product”

Mathematical representation of vector product
Consider two vectors and making an angle q with each other. Their vector product or cross product is defined as:
vector product of two vectors and is a third vector whose magnitude is equal to the product of the magnitudes of and and the sine of the angle between them. The direction of the product vector is perpendicular to the plane containing both the vectors.

Direction of third vector
The vector which represents the cross product or vector product is perpendicular to the plane containing vectors and and points in the direction in such a way as to make A , B and C vectors in order.
Direction of third vector C can be determined by using right hand rule:
Explanation

Example 1:
When we multiply two vector quantities force arm and force we get torque which is also a vector quantity. Therefore, we can say that torque is the vector product or cross product of force arm and force.

Example 2:
When we multiply two vector quantities velocity and magnetic flux density we get force which is also a vector quantity. Therefore, we can say that force is the vector product or cross product of velocity and magnetic flux density.