|
|
|
|
|
|
|
|
|
|
|
|
$$$\frac{5 \sqrt{34}}{34}\cdot \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle$$$
Ihre Eingabe
Berechne $$$\frac{5 \sqrt{34}}{34}\cdot \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle$$$.
Lösung
Multipliziere jede Komponente des Vektors mit dem Skalar:
$$${\color{Fuchsia}\left(\frac{5 \sqrt{34}}{34}\right)}\cdot \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle = \left\langle {\color{Fuchsia}\left(\frac{5 \sqrt{34}}{34}\right)}\cdot \left(1\right), {\color{Fuchsia}\left(\frac{5 \sqrt{34}}{34}\right)}\cdot \left(- \frac{12}{25}\right), {\color{Fuchsia}\left(\frac{5 \sqrt{34}}{34}\right)}\cdot \left(\frac{9}{25}\right)\right\rangle = \left\langle \frac{5 \sqrt{34}}{34}, - \frac{6 \sqrt{34}}{85}, \frac{9 \sqrt{34}}{170}\right\rangle$$$
Antwort
$$$\frac{5 \sqrt{34}}{34}\cdot \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle = \left\langle \frac{5 \sqrt{34}}{34}, - \frac{6 \sqrt{34}}{85}, \frac{9 \sqrt{34}}{170}\right\rangle\approx \left\langle 0.857492925712544, -0.411596604342021, 0.308697453256516\right\rangle$$$A