The vector product of two vectors **A** and **B** is defined as the vector **C **=** A **×**
B.**

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

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.

**Please click on the image below for an animation!**

We can find the Cartesian components of **C **=** A **×** B**
in terms of 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}