Proof involving cross products

1. Sep 2, 2009

lemmiwinks

So I'm an engineering student and we're doing some work with tensors and indicial notation, and I came across something that I know is true but couldn't think of how to prove. I don't need it for hw or anything it's just a curiosity thing. OK, so

Basically take a set of axes, 3 perpendicular vectors, call them A B and C
Prove (AXC)'dot'(BXC) = 0 (ie the vectors are perpendicular, X stands for cross product)

It seems like it should be really obvious but I can't think of how to solve it like a proof... I'm probably gonna feel like a moron when somebody answers but whatever.

2. Sep 2, 2009

rock.freak667

If A,B and C are perpendicular.

What vector does AxC give? What vector does BxC give? Knowing that when when you find the cross-product of two vectors, you get a vector perpendicular to the plane containing the two crossed vectors.

3. Sep 2, 2009

lemmiwinks

Yeah I guess it was a stupid question I was just trying to think of how I would write it down on paper.

4. Sep 2, 2009

rock.freak667

Well you could just write it as AxC =B and BxC=A, B.A = 0. You can probably expand (AxC).(BxC) and get it out. But that takes too much time in case you don't know what a.(bxc) equals.

5. Sep 3, 2009

Edgardo

Since you mentioned tensors and indices, are you supposed to use the http://folk.uio.no/patricg/teaching/a112/levi-civita/index.html" [Broken]?

Last edited by a moderator: May 4, 2017
6. Sep 9, 2009

LCKurtz

A X C is perpendicular to the plane of A and C so is parallel to B. B X C is perpendicular to B so it is perpendicular to A X C. That's why the dot product is 0.