# Thread: Simplify and prove, planes

1. ## Simplify and prove, planes

Hello.
I have some questions that I cannot figure out how to solve them.

Problem 3.5.29)
Simplify (u+v) x (u-v)

Problem 3.5.33)
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.

2. Originally Posted by algie
Problem 3.5.29)
Simplify (u+v) x (u-v)

Problem 3.5.33)
Prove: If a, b, c and d lie in the same plane, then
(a x b) x (c x d) = 0
For the first one use the distributive property twice.

For the second one realize that parallel vectors have cross product zero.
But why are $a\times b~\&~c\times d$ parallel?

3. The first)
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)

The second)
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!

4. Originally Posted by algie
The first)
The distrubutive property, two times?
u*(v+w) = u*v+u*w WRONG
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)CORRECT
$A\times(B+C)=A\times B + A\times C$

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