I am not currently in school, but need to relearn some vector algebra for an electrodynamics class. I have a textbook that I am using to teach myself the basics.

Here's the problem, in one section on the scalar triple product (A [tex]\cdot[/tex] (B X C)), it states that geometrically the magnitude of this (|A [tex]\cdot[/tex] (B X C)|)represents the volume of the parallelpiped generated by the 3 vectors A, B and C since |B X C| is the area of the base and |A cos ϴ|

is the height.

I get what they are saying, but mathematically it does not work out that way. Assume \vec{A} = (1x + 0y + 1z) and \vec{B} = (0x + 1y + 1z). The length (magnitude) of both A and B is \sqrt{2}. So the area of the base formed by these vectors would be 2; however, A x B = \sqrt{3}.

Can someone explain where I am going wrong? Or is the book wrong?