# Rearranging a cross product

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Hi all, simple question with possibly a not-so-simple answer. With three vectors, A, B and C, I have this equation and I want to find A: A x B = C A = ? Any ideas how I'd do that?

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If you have no other conditions, this problem is not well posed as there is no unique solution. C is perpendicular to the plane with A and B, and has the length |A|*|B|*sin( angle between A and B ). If you have C, you know the plane in which A should lay (the plane perpendicular to C). But the direction and length of A both determine the length of C. So you get many solutions, with the length of A and the angle between A and B being related to each other.

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Quote:
 Original post by hymermanHi all, simple question with possibly a not-so-simple answer. With three vectors, A, B and C, I have this equation and I want to find A:A x B = CA = ?Any ideas how I'd do that?

Expand it out and solve the system of linear equations?

There might be one but I don't remember a formula that negates B.

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Quote:
 Original post by dietepietIf you have no other conditions, this problem is not well posed as there is no unique solution.

Balls. That explains why I've been sat here scratching my head waving around pens sellotaped together at right-angles for the past three hours.

I'll have to find another way, thanks very much dietepiet :)

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If you know that the vectors are all perpendicular, as in many coordinate systems, and you know the length of B and C, your problem is well posed and there is a unique solution. Then A is just perpendicular to both B and C and has length |C|/|B|.

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For example of the ill-posedness, consider this:
(1,0,0)x(0,1,0)=(0,0,1), but also,
(1,1,0)x(0,1,0)=(0,0,1)

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