Evaluate scalar triple products

[DryRun]

http://s2.ipicture.ru/uploads/20111115/BiYq94IS.jpg

Here is the determinant for axb:
w x y z
1 -2 3 -4
-1 2 4 -5

Then, how to proceed?? Can someone please help?

 

[rock.freak667]

The wiki page may help you

http://en.wikipedia.org/wiki/Triple_product

 

[DryRun]

My confusion is how to get a 3x3 determinant when the vectors a, b and c are presented as being in R^4.
For example, when i make the determinant for c.(axb), i get:

c1 c2 c3 c4
a1 a2 a3 a4
b1 b2 b3 b4

But it's not possible to evaluate such a 3x4 determinant, right? And the question is requesting that i evaluate a 3x3 determinant.

Any ideas?

 

[HallsofIvy]

I guess the question is "How is the triple product of two vectors defined in R⁴"?

 

[DryRun]

I honestly have no idea, but this is really the entire question:
http://s2.ipicture.ru/uploads/20111115/BiYq94IS.jpg