Define and prove that where θ is the angle between and

Cross Product: The vector or cross product of two non-zero vectors and, denoted by, is defined as

where θ is the angle between and , 0≤θ≤π and is a unit vector perpendicular to both and, such that, and form a right handed system.

We have

is a unit vector

But, we have the dot product of two vectors and forming an angle θ as

Now, we divide these two equations.

Thus,