At right angles - in two or more dimensions.
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In a plane, each vector has only one orthogonal vector (well, two, if you count the negative of one of them). Are you sure you don't mean the normal vector which is orthogonal but outside the plane (in fact, orthogonal to the plane itself)?
The answer will depend on orthogonal to WHAT!
it means changing the mathematics information
yes. not sure of the proof though.
safrethyt