(%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 . . ."$