(* Change x,y,z to change the dimensions of the vector*)
x = 1;
y=2;
z=3;
v1 = Arrow[{{0,0,0},{x,y,z}}];

Show[Graphics3D[{Red,v1}],Axes->True,AxesOrigin->{0,0,0},Boxed->False,Ticks->{{{x,"a"}},{{y,"b"}},{{z,"c"}}}]

projXY = Arrow[{{0,0,0},{x,y,0}}];
zCoord = Arrow[{{x,y,0},{x,y,z}}];Show[Graphics3D[{{Red,v1},{Gray,projXY},{Blue,zCoord}}],Axes->True,AxesOrigin->{0,0,0},Boxed->False,Ticks->{{{x,"a"}},{{y,"b"}},{{z,"c"}}}]