We know from Flaming's Right Hand Rule how to calculate the direction of the magnetic force given the magnetic field and the velocity are in the same plane. Now suppose they are not in the same plane. As an example, consider a uniform magnetic field directed perpendicularly onto the screen and a charged particle moving on an inclined plane with angle X with the horizontal. What will be the direction of the magnetic force here?
I think Flaming's Right Hand Rule can only be applied when they are in the same plane because if they are not we cannot adjust our hand so that our fingers point to both of them. But I'm just a beginner in this field, so please correct me if I am wrong.
Best Answer
Two vectors (starting or shifted/imagined to start at the same point) always belong to the same plane, usually one plane. If the vectors are $A\to B$ and $A\to C$, just imagine that you connect $B,C$ by a straight line, thus completing a triangle, $ABC$. This triangle is already a clear "seed" of a plane, isn't it? The plane isn't necessary vertical, horizontal, or parallel to any other plane you may have thought about at the beginning but it is a plane nevertheless. There always exists a vector $\vec n$ that is orthogonal to the whole plane or, equivalently, that is orthogonal both to the vectors $A\to B$ and $A\to C$.
This is not really physics but rather geometry for the 10-year-olds.