$$$\frac{\sqrt{2}}{4}\cdot \left\langle 2, -2, 0\right\rangle$$$
この計算機は、手順を示しながら、ベクトル $$$\left\langle 2, -2, 0\right\rangle$$$ をスカラー $$$\frac{\sqrt{2}}{4}$$$ 倍します。
入力内容
$$$\frac{\sqrt{2}}{4}\cdot \left\langle 2, -2, 0\right\rangle$$$を計算せよ。
解答
ベクトルの各成分にスカラーを乗じる:
$$${\color{Chocolate}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left\langle 2, -2, 0\right\rangle = \left\langle {\color{Chocolate}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(2\right), {\color{Chocolate}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(-2\right), {\color{Chocolate}\left(\frac{\sqrt{2}}{4}\right)}\cdot \left(0\right)\right\rangle = \left\langle \frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2}, 0\right\rangle$$$
解答
$$$\frac{\sqrt{2}}{4}\cdot \left\langle 2, -2, 0\right\rangle = \left\langle \frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2}, 0\right\rangle\approx \left\langle 0.707106781186548, -0.707106781186548, 0\right\rangle$$$A