> # Section 11.1\
# Selected exercises -- some don't translate well to Maple
> # exercise 3\
# the next command asks for help on the pointplot command, ?plots gives the list of plot commands\
?pointplot\
# how to load the collection of plot commands \
with(plots):\
# plot the corners\
pointplot({[1,1,2],[3,4,5],[1,1,5],[1,4,2],[3,1,2],[1,4,5],[3,1,5],[3,4,2]},axes=normal,color=yellow);
--------------------------------------------------------------------------------
> # exercise 5\
# define a distance function\
dist := a -> sqrt(a[1]*a[1]+a[2]*a[2]+a[3]*a[3]);

                                          2       2       2
                    dist := a -> sqrt(a[1]  + a[2]  + a[3] )
--------------------------------------------------------------------------------
> A:=[-2,6,1];B:=[3,3,2]; C:=[1,4,4];

                                 A := [-2, 6, 1]

                                 B := [3, 3, 2]

                                 C := [1, 4, 4]
--------------------------------------------------------------------------------
> # need some vector stuff, load with the command\
with(linalg):\

> dist(add(A,B,1,-1));\


                                        1/2
                                      35
--------------------------------------------------------------------------------
> dist(add(A,C,1,-1));

                                        1/2
                                      22
--------------------------------------------------------------------------------
> dist(add(B,C,1,-1));

                                        3
--------------------------------------------------------------------------------
> # and since 9 + 22 != 35 this is an un-interesting triangle.\
# note the build in norm ( vector, 2)  function is our distance function\
norm(add(A,B,1,-1),2);

                                        1/2
                                      35
--------------------------------------------------------------------------------
> # Exercise 15\
eq1 := x^2 + y^2 + z^2 + 2*x + 8*y-4*z = 28;

                           2    2    2
                   eq1 := x  + y  + z  + 2 x + 8 y - 4 z = 28
--------------------------------------------------------------------------------
> eq2 := (x-h)^2+(y-k)^2+(z-l)^2=r^2;

                                 2          2          2    2
                   eq2 := (x - h)  + (y - k)  + (z - l)  = r
--------------------------------------------------------------------------------
> eq3:=expand(eq2);

                 2            2    2            2    2            2    2
         eq3 := x  - 2 x h + h  + y  - 2 y k + k  + z  - 2 z l + l  = r
--------------------------------------------------------------------------------
> solve({coeff(lhs(eq1),x,1)=coeff(lhs(eq3),x,1),coeff(lhs(eq1),y,1)=coeff(lhs(eq3),y,1),\
coeff(lhs(eq1),z,1)=coeff(lhs(eq3),z,1)},{h,k,l});

                             {h = -1, k = -4, l = 2}
--------------------------------------------------------------------------------
> coeff(coeff(coeff(lhs(eq3),x,0),y,0),z,0);

                                   2    2    2
                                  h  + k  + l
--------------------------------------------------------------------------------
> # an easier way uses the student package\
with(student);

 [D, Doubleint, Int, Limit, Lineint, Sum, Tripleint, changevar, combine,

     completesquare, distance, equate, extrema, integrand, intercept, intparts,

     isolate, leftbox, leftsum, makeproc, maximize, middlebox, middlesum,

     midpoint, minimize, powsubs, rightbox, rightsum, showtangent, simpson,

     slope, trapezoid, value]
--------------------------------------------------------------------------------
> completesquare(eq1,{x,y,z});

                           2               2          2
                    (z - 2)  - 21 + (y + 4)  + (x + 1)  = 28
--------------------------------------------------------------------------------
> "+(21=21);

                              2          2          2
                       (z - 2)  + (y + 4)  + (x + 1)  = 49
--------------------------------------------------------------------------------
> sqrt(rhs("));

                                        7
--------------------------------------------------------------------------------
>