Lösungen/Solutions/E1S1AlUe/Ex13

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

Ueb/Ex 1      W

V  =  
      1/6 Det[{{3, -1, 5}, {2, 3, 6}, {-5, -6, 4}}]

N[%]

Ueb/Ex 2      W

V  =  
      Det[{{3, -1, 5}, {2, 3, 6}, {-5, -6, z}}]

Solve[V == 50, {z}] // Flatten

N[%]

Ueb/Ex 3      L

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

r0 = {5, 1, 3};  a = {3, -1, 5};  b = {2, 3, 6};  
    n = Cross[a, b]

en = n/len[n]

N[en]

r[x_, y_, z_] := {x, y, z}

Φ[{x_, y_, z_}] := 
      en . r[x, y, z] + d;  Φ[{x, y, z}]

solv3 = 
      Solve[ Φ[r0] == 0, {d}] // Flatten

ΦNew[{x_, y_, z_}] := 
        en . r[x, y, z] + d  /.  solv3;
ΦNew[{x, y, z}]

c = {3, 4, 5}

OP0 = {5, 1, 6}

Remove[g]

g[t_] := OP0 + t c;  g[t]

tSg = 
      Solve[ ΦNew[g[t]] == 0, {t}] // Flatten

Sg = g[t] /. tSg

N[%]

gh[t_] := OP0  +  t n;  gh[t]

tSh = 
      Solve[ ΦNew[gh[t]] == 0, {t}] // Flatten

Sh = gh[t] /. tSh

N[%]

A =  1/2 len[Cross[Sg - Sh,  OP0 - Sh]]

N[%]