Lösungen / Solutions

1 exakt

a = {5, 4}; b = {6, 7}; 
    c = {{Cos[f], Sin[f]}, {-Sin[f], Cos[f]}};  c . a

c1[f_] := {{Cos[f], Sin[f]}, {-Sin[f], Cos[f]}}; 
    MatrixForm[c1[f]]

Solve[5 Cos[f] - 4 Sin[f] == 0, {f}]

Solve[5 /4 ==  Sin[f]/Cos[f], {f}] //  Flatten

fi = f /. N[%]

BStich = c1[fi] . {6, 7}

2 exakt

vLen[v_] := Sqrt[v . v]

a = {3, 4, 1}; b = {4, 5, 6}; c = Cross[a, b]

c = Cross[a, b]/vLen[Cross[a, b]]

N[%]

a + b + c

N[%]

a + b - c

N[%]

3 exakt

c = {2, -1, 3};
Cross[a, b] . c

Cross[a, b] . c/vLen[Cross[a, b]]

N[%]

vX = {x, y, z}

Solve[{a . vX == 1, b . vX == 2, c . vX == 3}, {x, y, z}]

N[%]

4 exakt