Question

The cross product of 2 vectors, A and B, gives a vector C that is perpendicular to the plane AB. But we can't always contain two vectors in a plane (so we can't always find a plane AB) right? Would the cross product be valid in this case? What would be the result of the cross product?

Thanks in advance

Answer 1

If there are two vectors A and B, we can always have a plane in which both vectors A and B lies. So, what i'm saying is ... You can always find a plane.

Let me try to put into this way : If you have two points, you can always find a line passing through these two points. Similarly, if you have vectors, i.e. lines, you can always have a plane containing those two lines or vectors.

So, this question is not valid and cross product exist in any case.

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I hope I'm able to convince you.

Thank you!