Question: Gram-Schmidt problem

Use the Gram-Schmidt process to transform the basis
 
           {Vector(3, {(1) = 0, (2) = 1, (3) = 1}), 

             Vector(3, {(1) = 1, (2) = 1, (3) = 1}), 

             Vector(3, {(1) = 1, (2) = 2, (3) = 3})}

for the Euclidean space R3 into an orthonormal basis for R3

                               
Show 3D result.

This is what was given to solve the problem, but it is not working.

> GramSchmidt2 := proc () 

local M, rows, numV, v, seqL, lstL, i, j, vlength; 

numV := nargs; 

print('Original set'); 

    seqL := NULL; 

if type(args[1], Matrix) and numV = 1 then 

    M := args[1]; 

   numV := LinearAlgebra[ColumnDimension](M); 

   rows := LinearAlgebra[RowDimension](M);

   if rows < numV then 

       WARNING("input  is a set of Linearly Dependent Vectors") end if; 

   for i to numV do 

      vi := Column(M, i); 

      vi:= convert(vi, Vector); 

      seqL := seqL, vi :

end do: 

else 

  rows := nops(args[1]); 

  if rows < numV then 

         WARNING("input  is a set of Linearly Dependent Vectors"); 

end if; 

 for i to numV do vi:= args[i]; 

vi := convert(vi, Vector); 

if nops(vi) ≠ rows then 

error "the lenght of inputed Vectors sould be the same";

 end if; 

seqL := seqL, vi;

end do;

 end if; 

print([seqL]); 

print('Orthogonal set'); 

if Norm(vi, 2) ≠ 0 then 

seqL := vi;

else

 seqL := NULL;

 end if; 

for j from 2 to numV do 

for i to j-1 do 

if Norm(vi, 2) ≠ 0 then 

vj := vj-Proj(vi, vj);

 end if;

 end do; 

if Norm(vj, 2) ≠ 0 then 

seqL := seqL, vj;

end if;

 end do; 

print([seqL]); 

print('Orthonormal set'); 

seqL := NULL; 

for j to numV do 

if Norm(vj, 2) ≠ 0 then 

vj:= vj/Norm(vj, 2); 

seqL := seqL, vj;

end if;

 end do; 

print([seqL]); 

lstL := [seqL]; 

return lstL;

 end proc;
> Proj := proc (u, v) 

return (u.v)*u/(u.u);

end proc;

> w1 :=<(0,1,1)> ;

> w2 := <(1,1,1)>;
> w3 := <(1,2,3)>;

>GramSchmidt2(w1, w2, w3)

> vectordisplay := proc () 

local numV, v, a, seqA, lstL, i, j; 

numV := nargs; with(plots); 

setoptions(color = red, scaling = constrained, style = line); 

numV := nargs; 

seqA := NULL; 

for i to numV do

vi:= args[i]; 

vi:= convert(vi, Vector); 

if nops(vi) = 3 then 

ai:= arrow(vi, shape = arrow, axes = normal) else error "only display 3d vectors" end if; 

seqA := seqA, ai;

end do; 

display(seqA);

 end proc;
> w1 := ;
         
> w2 := ;
           
> w3 := ;
           
> printf("Before ... "); 

vectordisplay(w1, w2, w3); 

printf("Normalizing..."); 

lstW := GramSchmidt2(w1, w2, w3); 

printf("After..."); 

vectordisplay(op(lstW));