> # hw 4 11.4\
# 22\
with(linalg):
Warning: new definition for   norm
Warning: new definition for   trace

> p:=[1,0,-1];q:=[2,4,5];r:=[3,1,7];\
orthogonal:=crossprod(add(q,p,1,-1),add(r,p,1,-1));\
areaoftriangle:=norm(orthogonal,2)/2;

                                 p := [1, 0, -1]

                                 q := [2, 4, 5]

                                 r := [3, 1, 7]

                           orthogonal := [ 26, 4, -7 ]

                                                   1/2
                          areaoftriangle := 1/2 741
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> # 26\
a:=[1,0,6];b:=[2,3,-8];c:=[8,-5,6];\
volume:=abs(dotprod(a,crossprod(b,c)));

                                 a := [1, 0, 6]

                                 b := [2, 3, -8]

                                 c := [8, -5, 6]

                                  volume := 226
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> #11.5\
# 12\
dotprod(add([0,1,1],[1,-1,6],1,-1),add([-4,2,1],[-1,6,2],1,-1));

                                        0
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> #23\
n:=[1,1,-1];\
dotprod([x,y,z],n) = dotprod([6,5,-2],n);

                                 n := [1, 1, -1]

                                 x + y - z = 13
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> # 38\
eqns:={x=1-t,y=t,z=1+t,z=1-2*x+y};\
solve(eqns,{x,y,z,t});

             eqns := {y = t, x = 1 - t, z = 1 + t, z = 1 - 2 x + y}

                          {x = 0, y = 1, z = 2, t = 1}
--------------------------------------------------------------------------------
>