Kurs:Vektor-Algebra/Multiplikation/Vektorprodukt Anwendungen

Sinus-Satz

${\vec {a}}+{\vec {b}}+{\vec {c}}=0$

${\vec {a}}\times {\vec {b}}={\vec {a}}\times {\vec {(}}0-a-c)$

${\vec {a}}\times {\vec {(}}-c)$

${\vec {c}}\times {\vec {a}}$

Andererseits:

${\vec {a}}\times {\vec {b}}={\vec {c}}\times {\vec {a}}={\vec {b}}\times {\vec {c}}$

${\vec {a}}\times {\vec {b}}={\vec {b}}\times {\vec {a}}={\vec {b}}\times {\vec {c}}$

Beträge:

$ab\cdot sin(\pi -\gamma )=ca\cdot sin(\pi -\beta )=bc\cdot sin(\pi -\alpha )$

${\frac {a}{sin\alpha }}={\frac {c}{sin\gamma }}={\frac {b}{sin\beta }}$