$$$\frac{1}{2}\cdot \left\langle \sqrt{2}, -1, 1\right\rangle$$$

$$$\frac{1}{2}\cdot \left\langle \sqrt{2}, -1, 1\right\rangle$$$を計算せよ。

ベクトルの各成分にスカラーを乗じる:

$$${\color{Magenta}\left(\frac{1}{2}\right)}\cdot \left\langle \sqrt{2}, -1, 1\right\rangle = \left\langle {\color{Magenta}\left(\frac{1}{2}\right)}\cdot \left(\sqrt{2}\right), {\color{Magenta}\left(\frac{1}{2}\right)}\cdot \left(-1\right), {\color{Magenta}\left(\frac{1}{2}\right)}\cdot \left(1\right)\right\rangle = \left\langle \frac{\sqrt{2}}{2}, - \frac{1}{2}, \frac{1}{2}\right\rangle$$$

$$$\frac{1}{2}\cdot \left\langle \sqrt{2}, -1, 1\right\rangle = \left\langle \frac{\sqrt{2}}{2}, - \frac{1}{2}, \frac{1}{2}\right\rangle\approx \left\langle 0.707106781186548, -0.5, 0.5\right\rangle$$$A