Volume of parallelepiped(Linear Algebra)

[Sheneron]

Homework Statement

Show that the volume of a parallelepiped having u,v, and w as adjacent sides is given by abs(u*(vXw)).

(The star means dot product)

I am not really sure how to solve this problem. I was thinking that Volume would equal norm(u)+norm(v)+norm(w), but I couldn't figure out anywhere to go from there. Can someone help me start this problem. Thanks.

 

[djeitnstine]

First you should realize the dot product of 2 vectors is also the area of a parallelogram. Then you should note that the height of the parallelepiped is the projection of the vertical line to the line orthagonal (this should give you a hint) of the 2 vectors.

 

[Sheneron]

Awesome, thanks