Lösungen/Solutions/
F1S1Ue/Ex16

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

Remove["Global`*"]

Ueb/Ex 1      W

Φ1 = (3  x + 2  y - 4  z + 5 == 
            0);
Φ2 = (-2 x + 5  y + 8  z - 7 == 
            0);

n1 = {3, 2, -4}

n2 = {-2, 5, 8}

n = Cross[n1, n2]

Ueb/Ex 2      W

r01 = {2, 1, 
          5};                       
\(	\(a1 = {3, 7, 6};\)\ \)
r02 = {-1, -1, 4};     
\(	\ \(a2 = {\(-1\), 5, 2};\)\)

vecLen[a_] := Sqrt[a . a]

A = vecLen[Cross[a1, a2]]

N[%]

en = Cross[a1, a2]/vecLen[Cross[a1, a2]]

c = r02 - r01

h = en . c

N[%]

V  =  A * h

Det[{a1, a2, c}]

Ueb/Ex 3      W

rΦ = {2, 1, 
          5} +  λ {3, 7, 6} + μ {-1, 5, 2}

nΦ = Cross[{3, 7, 6}, {-1, 5, 2}]

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

Solve[Φ[{2, 1, 5}] == 0, {d}] //  Flatten

Ueb/Ex 4      W

g1 = (2 x  +  3 y  -  5  == 0)

g2 = (α x  +  4 y  +  6  == 0)

Solve[{g1, g2}, {x, y}] // Flatten

a, b

Solve[-8 + 3 α == 0, {α}] //  
      Flatten