Math help please vectors?
Hey,
The task is: Prove geometrically that there are infinitely many orthogonal vectors for a given vector. Distinguish between vectors in space and vectors in the plane.
So I would say that there are infinitely many multiples of a vector that is orthogonal to a given vector, so that this orthogonal vector can be infinitely long and still be orthogonal to the given vector.
However, I don't understand what is meant by distinguishing between space and level.
I would appreciate it if someone could explain it to me.
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Your approach is correct, for the sake of completeness, you should still consider that there is an orthogonal vector at all. In the room you can then not only extend it, but also turn it. The axis of rotation is the predetermined vector (if it is not equal to the zero vector).
OK, I’m saving my answer 🙂
Thank you for the helpful answer! So I can understand that if I have a vector that is in a plane, that there are infinitely many vectors that exist orthogonally to this vector, however, I cannot rotate the orthogonal vector arbitrarily, since this is then possibly no longer in the plane? And in the room can I turn it? I don’t know if I understood that correctly