(%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"$