> # hw 3\
# 11.3 and 11.4\
with(linalg):
Warning: new definition for   norm
Warning: new definition for   trace

> # 31\
rad2degree:=proc (rad)\
   180*rad/Pi;\
end;\
a:=[1,2,2];\
directioncosines:=scalarmul(a,1/norm(a,2));\
for i from 1 to 3 do evalf(rad2degree(arccos(directioncosines[i]))); od;

rad2degree := proc(rad) 180*rad/Pi end


                                 a := [1, 2, 2]

                      directioncosines := [ 1/3, 2/3, 2/3 ]

                                   70.52877934

                                   48.18968509

                                   48.18968509
--------------------------------------------------------------------------------
> #39\
a:=[4,2,0];b:=[1,1,1];\
scalarprojection:=dotprod(a,b)/norm(a,2);\
vectorprojection:=scalarmul(a, scalarprojection/norm(a,2));

                                 a := [4, 2, 0]

                                 b := [1, 1, 1]

                                                   1/2
                          scalarprojection := 3/5 5

                       vectorprojection := [ 6/5, 3/5, 0 ]
--------------------------------------------------------------------------------
> # 11.4\
# 1\
a:=[1,0,1]; b:=[0,1,0];\
crossproduct:=crossprod(a,b);

                                 a := [1, 0, 1]

                                 b := [0, 1, 0]

                          crossproduct := [ -1, 0, 1 ]
--------------------------------------------------------------------------------
> # 9\
a:=[0, 1, 2]; b:=[3,1,0];\
axb:= crossprod(a,b);\
bxa := crossprod(b,a);

                                 a := [0, 1, 2]

                                 b := [3, 1, 0]

                              axb := [ -2, 6, -3 ]

                               bxa := [ 2, -6, 3 ]
--------------------------------------------------------------------------------
>