# Volume of a parallelepiped

1. Nov 26, 2007

### tronter

1. The problem statement, all variables and given/known data

Show that the volume of a parallelepiped with edges $$A,B,C$$ is given by $$A \cdot (B \times C)$$.

2. Relevant equations

3. The attempt at a solution

$$B \times C$$ is the area of a parallelogram. From here I would I deduce the above result?

2. Nov 26, 2007

### tronter

Is $$A$$ just the height?

3. Nov 26, 2007

You're right, in two dimensions x and y the area is A=|bxc|. The height is actually |a|*|cos(theta)|. Where theta is the angle between vector a, and the cross product of vectors b and c. I'll include a picture but I hope this helps analytically to prove it. V=|a dot product to (b cross product with c.

4. Nov 26, 2007