Lösungen/Solutions/E1S1AlUe/Ex14

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

Remove["Global`*"]

Ueb/Ex 1      W

vecLen[r_] := Sqrt[r . r]

r01 = {2, 1, 3};  r02 = {-3, -1, 1};  a = {1, -2, 1}; 
    b = {-2, 1, 4};  r = {x, y, z};

rΦ[{λ_, μ_}] :=  
      r01  +  1/
            2 (r02 - r01)  + λ a  +  μ b

n = Cross[a, b]

Φ[{x_, y_, z_}] :=  
      n . {x, y, z}/vecLen[n] +  C1;  Φ[r]

en = n/vecLen[n]

N[%]

solv1 = 
      Solve[Φ[r01  +  1/2 (r02 - r01)] == 0, {C1}] // 
        Flatten

Φ[r] /. solv1

N[%] // Expand

Ueb/Ex 2      W

a = {5, 2, 1};  b = {1, 4, 8};  c = {-2, y, 4}

V  =  Det[{a, b, c}]

Solve[V == 100, {y}] // Flatten

N[%]

Ueb/Ex 3      W

a = {2, 1, 3}; b = {-3, -1, 1}; c = {5, 2, 1};

d1 = Cross[Cross[a, b], c]

d2 = Cross[a, Cross[b, c]]

Cross[d1, d2]

Ueb/Ex 4      W

d0 = 
      Det[{{4, -2, 3}, {8, -2, 
            4}, {9, α, β}}]

Solve[{
4  x - 2  y + 3  z - 5 == 
            0, 
8  x - 2  y + 4  z - 6 == 
            0, 
9  x + α y + β z + 
              4 == 0}, {x, y, z}]  // Flatten