Is it necessary that in 3 dimensions, two vectors will always be coplanar ? My teacher told the class that in 3 dimensions two vectors are always coplanar. But what if we consider two non parallel and non intersecting vectors ? like the ones parallel to 2 skew lines how can these be co planar ?
Another example is consider a cube. Now take one vector that is along the face diagonal of the upper face of the cube and another one that is along the face diagonal of the bottom face (the diagonal that is not in the same direction as the other one). These 2 are not coplanar as well.