高等考試
111年
[電力工程] 工程數學
第 5 題
下列那一組 $\mathbb{R}^3$ 中之向量基於歐幾里得內積（Euclidean inner product）可作為規格化正交基底（orthonormal basis）？
- A $(\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}), (-\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}), (-\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}})$
- B $(\frac{1}{5}, \frac{1}{5}, \frac{1}{5}), (-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0), (\frac{1}{3}, \frac{1}{3}, -\frac{2}{3})$
- C $(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}), (-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0)$
- D $(\frac{2}{3}, -\frac{2}{3}, \frac{1}{3}), (\frac{2}{3}, \frac{1}{3}, -\frac{2}{3}), (\frac{1}{3}, \frac{2}{3}, \frac{2}{3})$