Is A Cross B Equal to Zero a Test for Orthogonal Cases?

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SUMMARY

The discussion clarifies that the expression A × B = 0 is not a test for orthogonality but rather indicates that the vectors A and B are parallel or one of them is the zero vector. In contrast, the dot product A · B = 0 definitively confirms that vectors A and B are orthogonal (perpendicular). The confusion arises from the distinction between the cross product, which results in a vector perpendicular to both A and B, and the dot product, which provides a scalar value indicating orthogonality.

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Philosophaie
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A cross B equals zero is a test for orthogonal cases.

If AxB=0 then A is perpendicular to B.
 
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Uh...is that a question?
 
Philosophaie said:
A cross B equals zero is a test for orthogonal cases.

If AxB=0 then A is perpendicular to B.
No, it's not. It is the dot product. If A and B are vectors, the [itex]A\cdot B= 0[/itex] if and only if they are orthogonal (perpendicular).

You are confusing this with the fact that if A and B are any two (three dimensional) vectors, then [itex]A\times B[/itex] is perpendicular to both A and B.
 

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