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$$$\frac{1}{2}\cdot \left\langle - \sin{\left(t \right)}, \sqrt{3}, \cos{\left(t \right)}\right\rangle$$$
Votre saisie
Calculer $$$\frac{1}{2}\cdot \left\langle - \sin{\left(t \right)}, \sqrt{3}, \cos{\left(t \right)}\right\rangle$$$.
Solution
Multipliez chaque coordonnée du vecteur par le scalaire :
$$${\color{DarkBlue}\left(\frac{1}{2}\right)}\cdot \left\langle - \sin{\left(t \right)}, \sqrt{3}, \cos{\left(t \right)}\right\rangle = \left\langle {\color{DarkBlue}\left(\frac{1}{2}\right)}\cdot \left(- \sin{\left(t \right)}\right), {\color{DarkBlue}\left(\frac{1}{2}\right)}\cdot \left(\sqrt{3}\right), {\color{DarkBlue}\left(\frac{1}{2}\right)}\cdot \left(\cos{\left(t \right)}\right)\right\rangle = \left\langle - \frac{\sin{\left(t \right)}}{2}, \frac{\sqrt{3}}{2}, \frac{\cos{\left(t \right)}}{2}\right\rangle$$$
Réponse
$$$\frac{1}{2}\cdot \left\langle - \sin{\left(t \right)}, \sqrt{3}, \cos{\left(t \right)}\right\rangle = \left\langle - \frac{\sin{\left(t \right)}}{2}, \frac{\sqrt{3}}{2}, \frac{\cos{\left(t \right)}}{2}\right\rangle\approx \left\langle - 0.5 \sin{\left(t \right)}, 0.866025403784439, 0.5 \cos{\left(t \right)}\right\rangle$$$A