The simplest way to graph vectors is to use the appropriate commands in the VectorCalculus package. I prefer the Student VectorCalculus package because it is more forgiving with respect to the need for defining coordinate systems and coordinate-variable names.
The commands to use are PlotVector and RootedVector. The PlotVector command will graph various kinds of vectors, including ones defined simply with angle brackets: <1,2,3>. The RootedVector command will attach a starting point to the definition of the vector so that you don't have to make the adjustments needed when using either of the "arrow" commands in Maple, one in the plottools package, and one in the plots package.
In addition to these two commands, I recommend the PositionVector and PlotPositionVector commands. The PositionVector command is for defining a curve or surface as a position vector. The PlotPositionVector command then draws the curve or surface, and admits the addition of arrows from a variety of vector fields defined along the curve or surface. These two commands are an extremely powerful and useful pair of visualization tools.
I have just completed an extensive project on surface curvature in which I installed the Student MultivariateCalculus package to get access to a CrossProduct and DotProduct command. I also used the alias command to define a shortcut to the commands I wanted in VectorCalculus. This way, I avoided the conflict between the simple dot and crossproduct operations in the MultivariateCalculus package, and the more entangled versions in VectorCalculus. So, I'd make calculations along the following lines.