Defination : The vector product or cross product of two vector $\vec{a}$ and $\vec{b}$ is another vector $\vec{c}$, whose magnitude is equal to product of magnitude of the two vectors and sine of the smaller angle between them. $OR$

If the product of two vector gives resultant vector quantity then this product is vector product. Suppose two vectors $\vec{a}$ and $\vec{b}$ and angle between them is $\theta$

$\therefore \text { Vector product } \vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \sin \theta \hat{n}$ $=a b \sin \theta \hat{n}$

where $|\vec{a}|=a$ and $|\vec{b}|=b$

and $\hat{n}$ is a unit vector perpendicular to the plane form by $\vec{a}$ and $\vec{b}$

The product is known as cross ${~ }\times$ product also.

Suppose $\vec{a} \times \vec{b}$ is denoted by $\vec{c}$ then

$\vec{c}=a b \sin \theta \hat{n}$

and magnitude of $c=a b \sin \theta$

Direction of $\vec{c}$ is perpendicular to the plane form by $\vec{a}$ and $\vec{b}$ and its direction is given by right hand screw rule.