Lösungen/Solutions/
B1S1Ue/Ex13

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A  =Anhang/  Annexe / Appendice

Remove["Global`*"]

Ueb/Ex 1      W

γ[α_, β_] := 
      ArcCos[Sqrt[1 - Cos[α]^2 - Cos[β]^2]]

rad[α_] := α 2 Pi / 360

γa = γ[rad[73], rad[31]]

γaDegree = γ[rad[73], 
            rad[31]] /(2 Pi) 360

% // N

γb=γ[rad[69], rad[64]]

γbDegree = γ[rad[69], 
            rad[64]] /(2 Pi) 360

% // N

va = {Cos[rad[73]], Cos[rad[31]], Cos[γa]}

vb = {Cos[rad[69]], Cos[rad[64]], Cos[γb]}

len[v_] := Sqrt[v . v]

φDegree = 
      ArcCos[va . vb/(len[va] len[vb])] /(2 Pi) 360

N[%]

Ueb/Ex 2      W

a = {3, 2, 4};  b = {-2, 1, 6};  OA = {2, 1, 3};

OB =  OA + a

OC =  OA + b

c = OB - OC

len[a]

N[%]

len[b]

N[%]

len[c]

N[%]

φ[va_, vb_] := 
      ArcCos[va . vb/(len[va] len[vb])] /(2 Pi) 360

α = φ[c, -b]

N[%]

β = φ[c, a]

N[%]

γ = φ[a, b]

N[%]

bOrth[λ_] := b + λ a

b . bOrth[λ]

solv2 = 
      Solve[b . bOrth[λ] == 0, {λ}]  //  
        Flatten

bOrth = bOrth[λ] /. solv2

b . bOrth

abOrth = a . bOrth/len[bOrth]; h = abOrth

A  =  1/2 len[a]* h

N[%]

Ueb/Ex 3      W

Remove[g, g1, a, t, n]

a =  {5, 3}/len[ {5, 3}]

N[%]

g[t_] := {0, 3} +  t a;  g[t]

g1[t_] := {0, 0} +  t a;  g1[t]

n = {-a[[2]], a[[1]]}

len[n]

norm[t_] := t n;

ParametricPlot[{g[t], g1[t], norm[t]}, {t, -3, 
          5}, 
AspectRatio -> 1.2];

sSolv =  Solve[norm[t1] == g[t], {t1, t}] // Flatten

S = norm[t1] /. sSolv

Remove[Cconst]

solv3 = 
      Solve[ n . {0, 3} + Cconst == 0, {Cconst}] // Flatten

Cconst = Cconst  /.  solv3

λ ( n . {x, y} + Cconst) == {A, B} . {x, y} + 
        1

solv31 = 
      Solve[λ Cconst == 1, {λ}] // Flatten

{A, B} = -((Sqrt[34])/15) n