Lösungen/Solutions/
F1S1Ue/Ex12

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

Remove["Global`@*"]

Ueb/Ex 1      W

rg1[t_] := {-2, 4} + t {7, 2};
rg2[t_] := {8, 3} + t {-4, 5};

s1a = 
      Solve[rg1[λ] == rg2[μ], {λ, μ}] // 
        Flatten

s1a // N

res1a = {rg1[λ], rg2[μ]} /. s1a

res1a // N

ParametricPlot[Evaluate[rg1[t]], {t, -4, 4}];

ParametricPlot[
        Evaluate[{rg1[t], rg2[t]}], {t, -4, 4}];

h[t_] := 
      rg1[t] + {-2, 7}/Sqrt[(-2)^2  +  7^2] 4

h[t] // N

ParametricPlot[
        Evaluate[{rg1[t], rg2[t], h[t]}], {t, -4, 4}];

s1b = 
      Solve[h[λ] == rg2[μ], {λ, μ}] // 
        Flatten

s1b // N

{h[λ], rg2[μ]} /. s1b  // N

φ =  
      ArcCos[{7, 2} . {-4, 5}/
          Sqrt[({7, 2} . {7, 2}) ({-4, 5} . {-4, 
                    5})]]

N[φ]

N[φ]/Degree

Ueb/Ex 2      W

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

A = aVert . b

aLen = a . a // Sqrt

aVertLen = aVert . aVert // Sqrt

% // N

Ueb/Ex 3      W

rg[t_] := {4, 1, 2} +  
          t {-3, 2, 1};
rh[t_] := {-1, 2, 0} +  t {1, -2, 4}

Solve[rg[λ] == rh[μ], {λ, μ}]

Ueb/Ex 4      W

a = {3, 2}; φ = Pi/3;
a1 = {3 Cos[φ] - 2  Sin[φ], 
        3  Sin[φ] + 2  Cos[φ]}

N[%]

Ueb/Ex 5      W

a = {1, 2, 3}

α = ArcCos[1/Sqrt[a . a]]

N[%]

β = ArcCos[2/Sqrt[a . a]]

N[%]

γ = ArcCos[3/Sqrt[a . a]]

N[%]

α1 = ArcCos[1/Sqrt[{1, 2} . {1, 2}]]

N[%]

Ueb/Ex 6      W

rg[t_] := {4, 1, 2} +  t {-3, 2, 1};

Θ[λ_, μ_] := {0, 0, 
          0} + λ {1, 0, 0} + μ {0, 1, 0}

Solve[
      rg[t] == Θ[λ, μ], {t, λ, μ}]

S = rg[-2]

Θ[10, -3]