<單選題>空間中有相異四點 \( A, B, C, D \),已知內積 \(\overset{\rightharpoonup}{AB} \cdot \overset{\rightharpoonup}{AC} = \overset{\rightharpoonup}{AB} \cdot \overset{\rightharpoonup}{AD}\)。試選出正確的選項。
(1) \(\overset{\rightharpoonup}{AB} \cdot \overset{\rightharpoonup}{CD} = 0\)
(2) \(\overset{\rightharpoonup}{AC} = \overset{\rightharpoonup}{AD}\)
(3) \(\overset{\rightharpoonup}{AB} \) 與 \(\overset{\rightharpoonup}{CD} \) 平行
(4) \(\overset{\rightharpoonup}{AD} \cdot \overset{\rightharpoonup}{BC} = 0\)
(5) \(A, B, C, D \) 四點在同一平面上。
答案
\(\overset{\rightharpoonup}{AB} \cdot \overset{\rightharpoonup}{AC} = \overset{\rightharpoonup}{AB} \cdot \overset{\rightharpoonup}{AD} \Rightarrow \overset{\rightharpoonup}{AB} \cdot (\overset{\rightharpoonup}{AD} - \overset{\rightharpoonup}{AC}) = 0 \Rightarrow \overset{\rightharpoonup}{AB} \cdot \overset{\rightharpoonup}{CD} = 0\), 故選(1)。 報錯
ChatGPT DeepSeek


