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$$$\frac{\sqrt{3}}{3}\cdot \left\langle 1, -1, 1\right\rangle$$$
Ihre Eingabe
Berechne $$$\frac{\sqrt{3}}{3}\cdot \left\langle 1, -1, 1\right\rangle$$$.
Lösung
Multipliziere jede Komponente des Vektors mit dem Skalar:
$$${\color{OrangeRed}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left\langle 1, -1, 1\right\rangle = \left\langle {\color{OrangeRed}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(1\right), {\color{OrangeRed}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(-1\right), {\color{OrangeRed}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(1\right)\right\rangle = \left\langle \frac{\sqrt{3}}{3}, - \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3}\right\rangle$$$
Antwort
$$$\frac{\sqrt{3}}{3}\cdot \left\langle 1, -1, 1\right\rangle = \left\langle \frac{\sqrt{3}}{3}, - \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3}\right\rangle\approx \left\langle 0.577350269189626, -0.577350269189626, 0.577350269189626\right\rangle$$$A