I have some questions that I cannot figure out how to solve them.
Simplify (u+v) x (u-v)
Prove: If a, b, c and d lie in the same plane, then
(a x b) x (c x d) = 0
The "x" meaning the crossproduct.
The distrubutive property, two times?
u*(v+w) = u*v+u*w
I do not really understand how to apply it to my problem.
Here is/was/// my approach at the problem:
(u+v) x (u-v)
u^2 -2uv +v^2
Facit says: 2(v x u)
Because they are perpendicular to the plane.
I mean, they both go up from the plane so I think thats why they are parallel.
There is no facit for this, but I think this makes sense.
Thank you for your help, much appreciated!