> restart;with(linalg):#Web stuff first
> u:=vector([a,b,c]);X:=vector([x,y,z]);
> X[1];X[2];X[3];u;X;print(u);print(X);
> dotprod(u,X);
> crossprod(u,X);crossprod(X,u);
> norm(X);
> norm(X,2);norm(X,4);# Maple does this for "advanced math" -- The absolute values because of Maple allows for the possibility of complex numbers.
> normalize(u);
> scalarmul(u,2);
> matadd(u,X);
> matadd(u,X,2,-1);#2*u-X
> 
> with(plottools);
> with(plots):#arrow(from-where, to-where, arrow-width, arrow-head-width, head-fraction, ...)
> A:=arrow([0,0],[10,10],.2,.4,.1,color=green);#another Maple annoyance, [0,0] can't be vector([0,0]);
> display(A);
> B:=arrow([0,0,0],[10,10,10],.2, .4, .1,color=red);
> display(B,orientation=[-40,70],axes=boxed);
> #Switch gears to planes, normals, projections -- Lecture.
>