A vector in SageMath is constructed by applying the vector command to a list. Lists are entered in square brackets with entries separated by commas, so the typical way to create a vector looks like this:
Notice that nothing was displayed. SageMath just put the vector u into memory. We can ask for it by calling it.
SageMath defaults to displaying vectors horizontally, which is different from how we normally write them by hand.
This is okay. You will get used to it quickly.
SageMath knows how to add, multiply by scalars, and form linear combinations, and the notation for it is just as easy as you would expect.
If you ask SageMath to plot a vector, you get this kind of picture:
And in two dimensions something similar...
If you find that you want a vector to have its tail someplace
that is not the origin, use the arrow command.
Note that SageMath cut off some of this plot! Also, I used some options
just to show them off. The arrow command works in three dimensions,