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Posted 21 December 2004 - 09:23 PM
Posted 21 December 2004 - 09:58 PM
Quote:
Original post by happybara
mathwolrd says:
for two 2d vectors U=(U_{x},U_{y}) V=(V_{x},V_{y})
the crossproduct is
U x V = U_{x}*V_{y}-U_{y}*V_{x}
Posted 21 December 2004 - 11:06 PM
Quote:
Okay, maybe I'm missing something here, but doens't a cross product between two vectors with the same number of components give you another vector with that number of components?
Posted 22 December 2004 - 02:24 AM
Posted 22 December 2004 - 02:34 AM
Posted 22 December 2004 - 05:25 AM
Quote:
Original post by Puzzler183
In general, for an n-dimensional cross product, you need n - 1 vectors (so that the vector orthogonal to them all can be found. For 3 dimensions, this makes it look nice since you have only two operands. Note that this is also implemented in Mathematica this way.
Quote:
Using the 2D cross product where you get (U.x*V.y-U.y*V.x) is just like doing a 3D one where the Z components are 0. However, the generalized definition does indeed give you (U.y, -U.x).
Posted 22 December 2004 - 05:41 AM
Posted 22 December 2004 - 05:53 AM
Quote:
Original post by ajas95
SomeFunction(A,B,C)=(A x B . C)
- return volume of paralelepiped(sp?)
(note that order of operands does not matter...)
Dmytry: by 'SomeFunction', you mean 'determinant' right? :)
And operand order doesn't matter, as long as they keep the same winding... i.e. dat(A,B,C) == det(B,C,A) != det(C,B,A)
Posted 22 December 2004 - 08:09 AM
Posted 22 December 2004 - 09:34 PM
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