Cross Product

Cross Product

Vector Product or Cross Product 
If \(\vec A\) and \(\vec B\) are two vectors and the angle between them is \(\theta\) then the cross product of these two vectors is given by \( \overrightarrow A \times \overrightarrow B = \left( {AB\sin \theta } \right)\hat{n} \) .
Where \(\hat n\) is unit vector perpendicular to the plane containing \( \overrightarrow A \,\,\& \,\overrightarrow B \).
           

    Cross product of  two vectors is a vector. 
* Direction is given by right hand cork screw rule or Right Hand Thumb Rule

Right handed screw rule : Imagine a right handed screw to be placed along the normal of the plane containing the two vectors. Rotate the cap of the screw from first vector to second vector through small angle between them, the direction of motion of the tip of the screw gives the direction of their vector product.

Right hand thumb rule : Imagine the normal to the plane of the two vectors to be held in the right hand with the thumb erect. If  the fingers are whirling in the direction from first vector to second vector through small angle between them, the direction of the thumb gives the direction of their vector product.