The vector product of two vectors **A** and **B** is defined as the vector **C** = **A**×
**B**.
**C** is perpendicular to both **A** and **B**, i.e. it is perpendicular to the plane that contains
both **A** and **B**.

The direction of **C** can be found by using the **right-hand rule**.

Let the fingers of your right hand point in the direction of **A**.

Orient the palm of your hand so that, as you curl your fingers, you can sweep them over to point in the
direction of **B**.

Your thumb points in the direction of **C** = **A** × **B**. Practice the
**right-hand rule **below! Use your mouse to change the
view.

The magnitude of **C** is C = A B sinθ, where θ
is the smallest angle between the directions of the vectors **A** and **B**.

If **A** and **B** are parallel or anti-parallel to each other, then
**C** = **A** × **B**= 0, since sinθ = 0.

If **A** and **B**
are perpendicular to each other, then sinθ = 1 and **C** has its maximum
possible magnitude.

The components of the vector **C** = **A**× **B** and its magnitude can also be
found algebraically, given the components of **A** and **B**.

C_{x }= A_{y}B_{z }- A_{z}B_{y}

C_{y }= A_{z}B_{x }- A_{x}B_{z}

C_{z }= A_{x}B_{y }- A_{y}B_{x}

|C| = (C_{x}^{2} + C_{y}^{2}+ C_{z}^{2})^{½}