(%i1) "AB Ebenengleichung in Parameterform"$
(%i2) "Aufgabe 1"$
(%i3) "P_02(0|6|-3)"$
(%i4) "P_10(3|0|0)"$
(%i5) "P_min47(-12|21|-6)"$
(%i6) "Aufgabe 2"$
(%i7) "Aufpunkt stuetzE_ABC"$
(%i8) stuetzE_ABC : transpose(matrix ([0.0,0.0,3.0]));
[ 0.0 ]
[ ]
(%o8) [ 0.0 ]
[ ]
[ 3.0 ]
(%i9) "Richtungsvektoren uvec und vvec"$
(%i10) uvecE_ABC : transpose(matrix ([3.0,0.0,-3.0]));
[ 3.0 ]
[ ]
(%o10) [ 0.0 ]
[ ]
[ - 3.0 ]
(%i11) vvecE_ABC : transpose(matrix ([0.0,3.0,-3.0]));
[ 0.0 ]
[ ]
(%o11) [ 3.0 ]
[ ]
[ - 3.0 ]
(%i12) "Ebenengleichung"$
(%i13) display(stuetzE_ABC + r * uvecE_ABC + s * vvecE_ABC)$
[ 0.0 ] [ 3.0 r ] [ 0.0 ] [ 3.0 r ]
[ ] [ ] [ ] [ ]
[ 0.0 ] + [ 0.0 ] + [ 3.0 s ] = [ 3.0 s ]
[ ] [ ] [ ] [ ]
[ 3.0 ] [ - 3.0 r ] [ - 3.0 s ] [ - 3.0 s - 3.0 r + 3.0 ]
(%i14) "Aufpunkt stuetzE_0"$
(%i15) stuetzE_0 : transpose(matrix ([0.0,0.0,0.0]));
[ 0.0 ]
[ ]
(%o15) [ 0.0 ]
[ ]
[ 0.0 ]
(%i16) "Richtungsvektoren uvec und vvec"$
(%i17) uvecE_0 : transpose(matrix ([3.0,0.0,-3.0]));
[ 3.0 ]
[ ]
(%o17) [ 0.0 ]
[ ]
[ - 3.0 ]
(%i18) vvecE_0 : transpose(matrix ([0.0,3.0,-3.0]));
[ 0.0 ]
[ ]
(%o18) [ 3.0 ]
[ ]
[ - 3.0 ]
(%i19) "Ebenengleichung"$
(%i20) display(stuetzE_0 + r * uvecE_0 + s * vvecE_0)$
[ 0.0 ] [ 3.0 r ] [ 0.0 ] [ 3.0 r ]
[ ] [ ] [ ] [ ]
[ 0.0 ] + [ 0.0 ] + [ 3.0 s ] = [ 3.0 s ]
[ ] [ ] [ ] [ ]
[ 0.0 ] [ - 3.0 r ] [ - 3.0 s ] [ - 3.0 s - 3.0 r ]
(%i21) "Aufgabe 3"$
(%i22) "Punktprobe"$
(%i23) "Punkt G"$
(%i24) G: transpose(matrix ([3.0,3.0,3.0]));
[ 3.0 ]
[ ]
(%o24) [ 3.0 ]
[ ]
[ 3.0 ]
(%i25) "Punkt H"$
(%i26) H: transpose(matrix ([6.0,9.0,0.0]));
[ 6.0 ]
[ ]
(%o26) [ 9.0 ]
[ ]
[ 0.0 ]
(%i27) "Punkt Q"$
(%i28) Q: transpose(matrix ([6.0,9.0,-12.0]));
[ 6.0 ]
[ ]
(%o28) [ 9.0 ]
[ ]
[ - 12.0 ]
(%i29) "Abstand Punkt G von Ebene E_ABC: d = 3.464101615138"$
(%i30) "Abstand Punkt H von Ebene E_ABC: d = 6.928203230276"$
(%i31) "Punkt Q liegt in der Ebene E_ABC"$
(%i32) "Aufgabe 4 => fehlt!"$
(%i33) "Aufgabe 5"$
(%i34) "Drei Punkte A, B, C der Ebene"$
(%i35) A : transpose(matrix ([3.0,0.0,0.0]));
[ 3.0 ]
[ ]
(%o35) [ 0.0 ]
[ ]
[ 0.0 ]
(%i36) B : transpose(matrix ([0.0,3.0,0.0]));
[ 0.0 ]
[ ]
(%o36) [ 3.0 ]
[ ]
[ 0.0 ]
(%i37) C : transpose(matrix ([3.0,3.0,3.0]));
[ 3.0 ]
[ ]
(%o37) [ 3.0 ]
[ ]
[ 3.0 ]
(%i38) "Aufpunkt stuetzvec"$
(%i39) stuetzF : transpose(matrix ([3.0,0.0,0.0]));
[ 3.0 ]
[ ]
(%o39) [ 0.0 ]
[ ]
[ 0.0 ]
(%i40) "Richtungsvektoren uvec und vvec"$
(%i41) uvecF : B - A;
[ - 3.0 ]
[ ]
(%o41) [ 3.0 ]
[ ]
[ 0.0 ]
(%i42) vvecF : C - A;
[ 0.0 ]
[ ]
(%o42) [ 3.0 ]
[ ]
[ 3.0 ]
(%i43) "Ebenengleichung"$
(%i44) display(stuetzF + r * uvecF + s * vvecF)$
[ 3.0 ] [ - 3.0 r ] [ 0.0 ] [ 3.0 - 3.0 r ]
[ ] [ ] [ ] [ ]
[ 0.0 ] + [ 3.0 r ] + [ 3.0 s ] = [ 3.0 s + 3.0 r ]
[ ] [ ] [ ] [ ]
[ 0.0 ] [ 0.0 ] [ 3.0 s ] [ 3.0 s ]
(%i45) "Aufgabe 6"$
(%i46) "Schnittgerade der Ebenen E_ABC und F"$
(%i47) display(transpose(matrix([0.0, 3.000000000000, -0.000000000000])) + r * transpose(matrix([-1.0,1.0,0.0])))$
[ 0.0 ] [ - 1.0 r ] [ - 1.0 r ]
[ ] [ ] [ ]
[ 3.0 ] + [ 1.0 r ] = [ 1.0 r + 3.0 ]
[ ] [ ] [ ]
[ -0.0 ] [ 0.0 ] [ 0.0 ]
(%i48) "Schnittwinkel alpha = 70.528779365509"$
(%i49) "Aufgabe 7 => LGS aufstellen - und loesen . . ."$