Elliott Beck
05/14/2023 · Senior High School
Exercice 1 Soient les vecteurs \( \overrightarrow{F_{1}}\left(\begin{array}{c}6 \\ 2 \\ -9\end{array}\right) \) et \( \overrightarrow{F_{2}}\left(\begin{array}{l}3 \\ 6 \\ 2\end{array}\right) \). 1. Calculer les normes de ces deux vecteurs. 2. Calculer le produit scalaire de ces deux vecteurs. 3. Calculer le produit vectoriel de ces deux vecteurs. 4. En déduire l'angle entre les deux vecteurs. Donner le résultat au degré près.
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1. Normes : \( \| \overrightarrow{F_{1}} \| = 11 \), \( \| \overrightarrow{F_{2}} \| = 7 \).
2. Produit scalaire : \( \overrightarrow{F_{1}} \cdot \overrightarrow{F_{2}} = 12 \).
3. Produit vectoriel : \( \overrightarrow{F_{1}} \times \overrightarrow{F_{2}} = \begin{pmatrix} 58 \\ -39 \\ 30 \end{pmatrix} \).
4. Angle : \( \theta \approx 67^\circ \).
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