with(LinearAlgebra);

# define main function
main := proc()

    print("Maple output");
    print("Chapter 2");
    prob05();
end;

prob05  := proc()
local a,b,c,d,e,m_a,m_b,m_c,m_d,m_e,d_a,d_b,d_c,d_d,d_e,dd_a,dd_b,dd_c,dd_d,dd_e;

    a := <4.0,-3.0,0.0>;
    b := <6.0,8.0,0.0>;

    print("Problem 5");
    print("a := ", a);
    print("b := ", b);
    c := a + b;
    d := b - a;
    e := a - b;
    f := <2.0,-3.0,7.0>;
    g := <12.0,45.0,-8.0>;
    h := <-5.0,-3.0,42.0>;

    print("c := ", c);
    print("d := ", d);
    print("e := ", e);
    m_a := mag(a);
    m_b := mag(b);
    m_c := mag(c);
    m_d := mag(d);
    m_e := mag(e);
    print("magnitude of a := ", m_a);
    print("magnitude of b := ", m_b);
    print("magnitude of c := ", m_c);
    print("magnitude of d := ", m_d);
    print("magnitude of e := ", m_e);
    d_a := direction_r(a);
    d_b := direction_r(b);
    d_c := direction_r(c);
    d_d := direction_r(d);
    d_e := direction_r(e);
    print("direction in radians of a := ", d_a);
    print("direction in radians of b := ", d_b);
    print("direction in radians of c := ", d_c);
    print("direction in radians of d := ", d_d);
    print("direction in radians of e := ", d_e);
    dd_a := direction_d(a);
    dd_b := direction_d(b);
    dd_c := direction_d(c);
    dd_d := direction_d(d);
    dd_e := direction_d(e);
    print("direction in degrees of a := ", dd_a);
    print("direction in degrees of b := ", dd_b);
    print("direction in degrees of c := ", dd_c);
    print("direction in degrees of d := ", dd_d);
    print("direction in degrees of e := ", dd_e);

    print("a.a",dot(a,a));
    print("a.b",dot(a,b));
    print("b.a",dot(b,a));
    print("a.c",dot(a,c));
    print("d.a",dot(d,a));
    print("a.e",dot(a,e));
    print("e.a",dot(e,a));
    
    print("axa",cross(a,a));
    print("axb",cross(a,b));
    print("bxa",cross(b,a));
    print("axc",cross(a,c));
    print("dxa",cross(d,a));
    print("axe",cross(a,e));
    print("exa",cross(e,a));
    
    print("fxg",cross(f,g));
    print("fxh",cross(f,h));
    print("gxh",cross(g,h));
    print("gxf",cross(g,f));
    print("hxf",cross(h,f));
    print("hxg",cross(h,g));

    af := <fx,fy,fz>;
    ag := <gx,gy,gz>;
    print("afxag",cross(af,ag));


end;

dot := proc(a,b)
local b_t,m,r;
    b_t := b^%T;   # transpose
    r := b_t . a ;   # dot product
end;

cross := proc(a,b)
local r;
    r := a &x b;   # cross product
end;





mag := proc(a)
local a_t,m,r_m;
    a_t := a^%T;   # transpose
    m := a_t . a ;   # dot product
    r_m := sqrt(m);
end;

direction_r := proc(a)
local dir;
    
    dir := arctan(a[2],a[1]);

end;

direction_d := proc(a)
local dir;
    
    dir := arctan(a[2],a[1]) * 180.0 / Pi;

end;




# call main
main();