On Wed, 06 Dec 2000 09:09:28 -0800, Josh English wrote:
>I thought that the area of the parallelogram was equal to the dot product. I
>seem to remember that we were able to find the area with some simple vector
>calculation. Too bad my book is at home.

Nope, the dot product is more closely related to the projection of one
vector onto another [the length of the projection of b onto a is 
vdot(a,b)/vlength(b)].  The length of the cross product is related to 
the orthogonal component [the length of the component of b orthogonal 
to a is vlength(vcross(a,b))/vlength(a)].

Since the area of a parallelogram is base (length of a) times height
(length of the component of b orthogonal to a) it turns out that the 
area of the parallelogram is exactly the length of the cross product.  
In my experience, this fact is rarely useful, but the two above often
are.

-- 
Ron Parker   http://www2.fwi.com/~parkerr/traces.html
My opinions.  Mine.  Not anyone else's.

Post a reply to this message