sqrt(3)/3 * ⟨1, -1, 1⟩

Laskin kertoo vektorin $$$\left\langle 1, -1, 1\right\rangle$$$ skalaarilla $$$\frac{\sqrt{3}}{3}$$$ ja näyttää vaiheet.

Syötteesi

Laske $$$\frac{\sqrt{3}}{3}\cdot \left\langle 1, -1, 1\right\rangle$$$.

Ratkaisu

Kerro vektorin jokainen koordinaatti skalaarilla:

$$${\color{BlueViolet}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left\langle 1, -1, 1\right\rangle = \left\langle {\color{BlueViolet}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(1\right), {\color{BlueViolet}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(-1\right), {\color{BlueViolet}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(1\right)\right\rangle = \left\langle \frac{\sqrt{3}}{3}, - \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3}\right\rangle$$$

Vastaus

$$$\frac{\sqrt{3}}{3}\cdot \left\langle 1, -1, 1\right\rangle = \left\langle \frac{\sqrt{3}}{3}, - \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3}\right\rangle\approx \left\langle 0.577350269189626, -0.577350269189626, 0.577350269189626\right\rangle$$$A

Please try a new game Rotatly