# vector operations between a two-dimensional and a three-dimensional vectors

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.

• 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. – user53153 Mar 5 '13 at 5:52