Explain the cross product of two vectors.

(N/A) Definition: The vector product or cross product of two vectors $\vec{a}$ and $\vec{b}$ is another vector $\vec{c}$,whose magnitude is equal to the product of the magnitudes of the two vectors and the sine of the smaller angle between them.
If the product of two vectors results in a vector quantity,then this product is called a vector product. Suppose there are two vectors $\vec{a}$ and $\vec{b}$ and the angle between them is $\theta$.
Therefore,the vector product is defined as $\vec{a} \times \vec{b} = |\vec{a}| |\vec{b}| \sin \theta \hat{n} = ab \sin \theta \hat{n}$,where $|\vec{a}| = a$ and $|\vec{b}| = b$.
Here,$\hat{n}$ is a unit vector perpendicular to the plane formed by $\vec{a}$ and $\vec{b}$.
This product is also known as the cross product $(\times)$.
If $\vec{a} \times \vec{b}$ is denoted by $\vec{c}$,then $\vec{c} = ab \sin \theta \hat{n}$.
The magnitude of the resulting vector is $c = ab \sin \theta$.
The direction of $\vec{c}$ is perpendicular to the plane containing $\vec{a}$ and $\vec{b}$,and its direction is determined by the right-hand screw rule.