load (draw);
load (vector_rebuild);

listarith : true;
doallmxops : true;
A : [2,0,0];
C : [0.8,0.5,2.5];
B : [1,2,0.5];
nullp : [0,0,0];

/* n ist der Normalenvektor der Ebene nullp, A, B */
  n : A~B;
/* f n*C / |n|  */
/* f ist die Länge der Projektion von C auf n */
  f : lsum(i,i,maplist("*",n,C)) / |n|;
/* NC ist der Lotpunkt des Lotes von C auf n */
  NC : n*f/|n|;

  str1 : strim("\"", string("set label '{/=25 @_{/=25 a}^{/=15 ->}}' at "));
  label1 : concat (str1, A[1]+0.2, ",", A[2], ",", A[3]);
  /**/
  str2 : strim("\"", string("set label '{/=25 @_{/=25 b}^{/=15 ->}}' at "));
  label2 : concat (str2, B[1]+0.2, ",", B[2], ",", B[3]);
  /**/
  str3 : strim("\"", string("set label '{/=25 @_{/=25 c}^{/=15 ->}}' at "));
  label3 : concat (str3, C[1]+0.2, ",", C[2], ",", C[3]);
  /**/
  str4 : strim("\"", string("set label '{/=25 @_{/=25 n}^{/=15 ->}}' at "));
  label4 : concat (str4, n[1], ",", n[2], ",", n[3]+0.4);
  /**/
  str5 : strim("\"", string("set label '{/=25 L}' at "));
  label5 : concat (str5, NC[1]-0.2, ",", NC[2], ",", NC[3]);
  /**/

draw3d (
  line_width = 2,
  /*
  xrange = [-0.5, 5],
  yrange = [-0.5, 5],
  zrange = [-0.5, 5],
  */
  points_joined = true,
  point_size = 1,
  point_type = none,
  transparent = false,
  head_length = 0.1,
  color = red,
  vector (nullp, A),
  color = blue,
  vector (nullp, B),
  color = green,
  vector (nullp, C),
  color = black,
  vector (nullp, n),
  points ([C, NC]),
  /* */
  xtics = false,
  ytics = false,
  ztics = false,
  user_preamble = [
                "set noborder", 
                 label1, label2, label3, label4, label5 
                ],
  /* view = [91, 60], */
  dimensions = [1200, 1200],
  file_name = "vol",
  /* terminal = eps_color */
  terminal = png 
);