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$$$\frac{\sqrt{3}}{3}\cdot \left\langle 1, -1, 1\right\rangle$$$
入力内容
$$$\frac{\sqrt{3}}{3}\cdot \left\langle 1, -1, 1\right\rangle$$$を計算せよ。
解答
ベクトルの各成分にスカラーを乗じる:
$$${\color{SaddleBrown}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left\langle 1, -1, 1\right\rangle = \left\langle {\color{SaddleBrown}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(1\right), {\color{SaddleBrown}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(-1\right), {\color{SaddleBrown}\left(\frac{\sqrt{3}}{3}\right)}\cdot \left(1\right)\right\rangle = \left\langle \frac{\sqrt{3}}{3}, - \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3}\right\rangle$$$
解答
$$$\frac{\sqrt{3}}{3}\cdot \left\langle 1, -1, 1\right\rangle = \left\langle \frac{\sqrt{3}}{3}, - \frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3}\right\rangle\approx \left\langle 0.577350269189626, -0.577350269189626, 0.577350269189626\right\rangle$$$A