.I have a quick conceptual question regarding vectors in 3-space. Say we are given vector A, and vector B, and we are told the dot product of said vectors is 0. We could deduce that they are at 90 degrees relative to each other. If the question takes this one step further and asks for a vector C that is also perpendicular to both A and B, we would merely take the cross product of AxB=C, and C would be the answer.
This would only be true if the vectors AxB and C have the same magnitude and direction. That is,
and must be a Right hand system of vectors.
If we were to multiply C by -1, would we also get another vector that is also at 90 degrees to those vectors? I would presume there would be two vectors at 90 degrees to A and B, one up and one down.