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# Vector Quadruple Products anyone? watch

1. Oh how I loathe geometry...

Show that
(axb).(cxd) = (b.d)(a.c) - (b.c)(a.d)

any help would be great.

[EDIT] Oh wait, I just found it in a book. Hooray! That was a bit of a waste of your time reading this, so here's a bit of for your troubles.

[EDIT AGAIN] hmm, where does (axb)x(cxd) lie in relation to the planes through O spanned by a&b, and c&d??
2. I think...

axb is perpendicular to the plane spanned by a and b, and similarly for cxd, so (axb)x(cxd) is perpendicular to each of these and is therefore the direction of the line of the intersection of the two planes. Because the lines go through the origin, then it is infact the line of intersection, not just the direction.

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Updated: November 11, 2004
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