回復 31# enlighten0626 的帖子
如圖，已知正四面體\(ABCD\)中，\(\displaystyle \overline{AE}=\frac{1}{4}\overline{AB}\)，\(\displaystyle \overline{CF}=\frac{1}{4}\overline{CD}\)。設向量\(\vec{DE}\)與向量\(\vec{BF}\)的夾角為\(\theta\)，求\(sin \theta\)的值為何？
(A)\(\displaystyle \frac{1}{13}\) (B)\(\displaystyle \frac{4}{13}\) (C)\(\displaystyle \frac{\sqrt{26}}{13}\) (D)\(\displaystyle \frac{\sqrt{153}}{13}\)
[解答]
小弟的做法是定義空間座標
C(0,0,0)、D(4,0,0)、B(2,2\(\sqrt{3}\),0)、A(2,\(\frac{2\sqrt{3}}{3}\),\(\frac{4\sqrt{6}}{3}\))
然後用內積的定義先解出\(cos\)，再解\(sin\)
