(%i1) "Cornelsen, S. 143/Nr. 39a)"$ (%i2) "Drei Punkte A, B, C der Ebene"$ (%i3) A : transpose(matrix ([6.0,2.0,6.0])); [ 6.0 ] [ ] (%o3) [ 2.0 ] [ ] [ 6.0 ] (%i4) B : transpose(matrix ([6.0,6.0,2.0])); [ 6.0 ] [ ] (%o4) [ 6.0 ] [ ] [ 2.0 ] (%i5) C : transpose(matrix ([3.0,6.0,6.0])); [ 3.0 ] [ ] (%o5) [ 6.0 ] [ ] [ 6.0 ] (%i6) "Aufpunkt stuetzvec"$ (%i7) stuetzE1 : transpose(matrix ([6.0,2.0,6.0])); [ 6.0 ] [ ] (%o7) [ 2.0 ] [ ] [ 6.0 ] (%i8) "Richtungsvektoren uvec und vvec"$ (%i9) uvecE1 : B - A; [ 0.0 ] [ ] (%o9) [ 4.0 ] [ ] [ - 4.0 ] (%i10) vvecE1 : C - A; [ - 3.0 ] [ ] (%o10) [ 4.0 ] [ ] [ 0.0 ] (%i11) "Ebenengleichung"$ (%i12) display(stuetzE1 + r * uvecE1 + s * vvecE1)$ [ 6.0 ] [ 0.0 ] [ - 3.0 s ] [ 6.0 - 3.0 s ] [ ] [ ] [ ] [ ] [ 2.0 ] + [ 4.0 r ] + [ 4.0 s ] = [ 4.0 s + 4.0 r + 2.0 ] [ ] [ ] [ ] [ ] [ 6.0 ] [ - 4.0 r ] [ 0.0 ] [ 6.0 - 4.0 r ] (%i13) "Drei Punkte A, B, C der Ebene"$ (%i14) A : transpose(matrix ([0.0,0.0,0.0])); [ 0.0 ] [ ] (%o14) [ 0.0 ] [ ] [ 0.0 ] (%i15) B : transpose(matrix ([0.0,0.0,6.0])); [ 0.0 ] [ ] (%o15) [ 0.0 ] [ ] [ 6.0 ] (%i16) C : transpose(matrix ([6.0,6.0,0.0])); [ 6.0 ] [ ] (%o16) [ 6.0 ] [ ] [ 0.0 ] (%i17) "Aufpunkt stuetzvec"$ (%i18) stuetzE2 : transpose(matrix ([0.0,0.0,0.0])); [ 0.0 ] [ ] (%o18) [ 0.0 ] [ ] [ 0.0 ] (%i19) "Richtungsvektoren uvec und vvec"$ (%i20) uvecE2 : B - A; [ 0.0 ] [ ] (%o20) [ 0.0 ] [ ] [ 6.0 ] (%i21) vvecE2 : C - A; [ 6.0 ] [ ] (%o21) [ 6.0 ] [ ] [ 0.0 ] (%i22) "Ebenengleichung"$ (%i23) display(stuetzE2 + r * uvecE2 + s * vvecE2)$ [ 0.0 ] [ 0.0 ] [ 6.0 s ] [ 6.0 s ] [ ] [ ] [ ] [ ] [ 0.0 ] + [ 0.0 ] + [ 6.0 s ] = [ 6.0 s ] [ ] [ ] [ ] [ ] [ 0.0 ] [ 6.0 r ] [ 0.0 ] [ 6.0 r ] (%i24) "Schnittgerade der Ebenen E1 und E2"$ (%i25) display(transpose(matrix([0.0, 0.000000000000, 16.000000000000])) + r * transpose(matrix([-3.0,-3.0,7.0])))$ [ 0.0 ] [ - 3.0 r ] [ - 3.0 r ] [ ] [ ] [ ] [ 0.0 ] + [ - 3.0 r ] = [ - 3.0 r ] [ ] [ ] [ ] [ 16.0 ] [ 7.0 r ] [ 7.0 r + 16.0 ] (%i26) "Schnittwinkel alpha = 83.034722718821"$ (%i27) "Nr. 39b)"$ (%i28) "Drei Punkte A, B, C der Ebene"$ (%i29) A : transpose(matrix ([0.0,0.0,3.0])); [ 0.0 ] [ ] (%o29) [ 0.0 ] [ ] [ 3.0 ] (%i30) B : transpose(matrix ([6.0,0.0,0.0])); [ 6.0 ] [ ] (%o30) [ 0.0 ] [ ] [ 0.0 ] (%i31) C : transpose(matrix ([0.0,3.0,0.0])); [ 0.0 ] [ ] (%o31) [ 3.0 ] [ ] [ 0.0 ] (%i32) "Aufpunkt stuetzvec"$ (%i33) stuetzE3 : transpose(matrix ([0.0,0.0,3.0])); [ 0.0 ] [ ] (%o33) [ 0.0 ] [ ] [ 3.0 ] (%i34) "Richtungsvektoren uvec und vvec"$ (%i35) uvecE3 : B - A; [ 6.0 ] [ ] (%o35) [ 0.0 ] [ ] [ - 3.0 ] (%i36) vvecE3 : C - A; [ 0.0 ] [ ] (%o36) [ 3.0 ] [ ] [ - 3.0 ] (%i37) "Ebenengleichung"$ (%i38) display(stuetzE3 + r * uvecE3 + s * vvecE3)$ [ 0.0 ] [ 6.0 r ] [ 0.0 ] [ 6.0 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 ] (%i39) "Drei Punkte A, B, C der Ebene"$ (%i40) A : transpose(matrix ([6.0,6.0,0.0])); [ 6.0 ] [ ] (%o40) [ 6.0 ] [ ] [ 0.0 ] (%i41) B : transpose(matrix ([6.0,3.0,0.0])); [ 6.0 ] [ ] (%o41) [ 3.0 ] [ ] [ 0.0 ] (%i42) C : transpose(matrix ([0.0,6.0,2.0])); [ 0.0 ] [ ] (%o42) [ 6.0 ] [ ] [ 2.0 ] (%i43) "Aufpunkt stuetzvec"$ (%i44) stuetzE4 : transpose(matrix ([6.0,6.0,0.0])); [ 6.0 ] [ ] (%o44) [ 6.0 ] [ ] [ 0.0 ] (%i45) "Richtungsvektoren uvec und vvec"$ (%i46) uvecE4 : B - A; [ 0.0 ] [ ] (%o46) [ - 3.0 ] [ ] [ 0.0 ] (%i47) vvecE4 : C - A; [ - 6.0 ] [ ] (%o47) [ 0.0 ] [ ] [ 2.0 ] (%i48) "Ebenengleichung"$ (%i49) display(stuetzE4 + r * uvecE4 + s * vvecE4)$ [ 6.0 ] [ 0.0 ] [ - 6.0 s ] [ 6.0 - 6.0 s ] [ ] [ ] [ ] [ ] [ 6.0 ] + [ - 3.0 r ] + [ 0.0 ] = [ 6.0 - 3.0 r ] [ ] [ ] [ ] [ ] [ 0.0 ] [ 0.0 ] [ 2.0 s ] [ 2.0 s ] (%i50) "Schnittgerade der Ebenen E3 und E4"$ (%i51) display(transpose(matrix([0.0, 1.000000000000, 2.000000000000])) + r * transpose(matrix([-6.0,1.0,2.0])))$ [ 0.0 ] [ - 6.0 r ] [ - 6.0 r ] [ ] [ ] [ ] [ 1.0 ] + [ 1.0 r ] = [ 1.0 r + 1.0 ] [ ] [ ] [ ] [ 2.0 ] [ 2.0 r ] [ 2.0 r + 2.0 ] (%i52) "Schnittwinkel alpha = 42.450155542891"$