Lösungen / Solutions

1

s = 
      Solve[{x, y, 
              z} == {-2, 4, 
                1} + λ {1, 0, 1} + μ {-3, 3, 5}, {x, y, z}] // 
        Flatten

Cross[{1, 0, 1}, {-3, 3, 5}] . {x, y, z}

-3 x - 8 y + 3 z == d /. {x -> -2, y -> 4, 
        z -> 1}

(-3 x - 8 y + 3 z)/(-23) == 1

((-3 x - 8 y + 3 z)/(-23) == 1) /. s  // 
      Simplify

2

g =  (2 x - 4 y + 3 z + 8 == 0)

s1 = Solve[g /. {y -> 0, z -> 0}, {x}] // Flatten

op1 = {x, y, z} /. {x -> -4, y -> 0, 
          z -> 0}

s2 = Solve[g /. {x -> 0, z -> 0}, {y}] // Flatten

op2 = {x, y, z} /. {x -> 0, y -> 2, z -> 0}

s3 = Solve[g /. {x -> 0, y -> 0}, {z}] // Flatten

op3 = {x, y, z} /. {x -> 0, y -> 0, 
          z -> -(8/3)}

{x, y, z} = 
      op1 + λ (op2 - op1)  +  μ (op3 - 
              op1)

3

Remove[x, y, z, g1, g2]

{g1, g2}

g1 =  (2 x - 4 y + 3 z + 8 == 
            0); 
g2 =  (2 x + 5 y - 4 z + 4 == 
            0);
Solve[{g1, g2}, {x, y}] /. z -> 0

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