Lösungen

p1 = {0, -4, 0};
p2 = {0, 0, 2};
q1 = {0, 0, 6};
q2 = {0, 4, 0};
q3 = {7, 9, -4};
g[t_] := p1 + t (p2 - p1);
e[λ_, μ_] := 
        q1 + λ (q2 - q1) + μ (q3 - 
                q1);
Solve[
      g[t] == e[λ, μ], {t, λ, μ}]

s1 = g[3/2]

s2 = {4, 0, 8}; s3 = {6, 6, 6}; 
    s4 = {1, 3, 8};
1/6  Det[{s2 - s1, s3 - s1, s4 - s1}]

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

Det[{q2 - q1, q3 - q1, s4 - q1}]/
      vLen[Cross[q3 - q1, q2 - q1]]

Abs[N[%]]