If you have a two-dimensional and a three-dimensional vectors, are vector operations (like dot product, cross product, addition, etc) defined between these two vectors? I though that since two-dimensional vectors can be written as three dimensional vectors with third component being zero, this is possible.
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$\begingroup$ If you write vectors as $2i-4j+3k$, it even comes naturally to do exactly that. A two-dimensional vector looks just like a 3d vector with the last component zero. $\endgroup$ – user53153 Mar 5 '13 at 5:52
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Depends how nitpicky you want to be. If you can embed the two-dimensional vector into a subspace of the three-dimensional space, then of course there is a natural way to extend it. Depends on what you want to do!
