# Cross Products relation to area.

1. Apr 22, 2005

### mkkrnfoo85

"The area of a parallelogram spanned by two vectors, v1 and v2, is ||v1 X v2||."

Would someone help me understand why this is true?

2. Apr 22, 2005

### Pyrrhus

Imagine a paralllelogram, and imagine 2 vectors V1, and V2, which have a Theta angle between them. Now You know the magnitude or modulus of the resultant vector of the cross product is given by $|V_{1}||V_{2}| \sin{\theta}$, imagine V2 is a horizontal vector (only a component of x), so it will be a side of the parallelogram (the base), now imagine V1 is directed at a theta angle, if you do V1sin theta, you will get the height of the parallelogram, so base times height equals area.

3. Apr 22, 2005

### mkkrnfoo85

ah. That makes a lot of sense. Thanks
(I kinda forgot about |v1||v2|sin(theta).. The things I dont see... )