Question

[Pham Trong Bach]

Cho tứ diện ABCD. Nếu AB ⊥CD, AC ⊥ BD và BC ⊥ AD thì:

A.  $\stackrel{\to }{AB}.\stackrel{\to }{AC} \ne \stackrel{\to }{AC}.\stackrel{\to }{AD} = \stackrel{\to }{AB}.\stackrel{\to }{AD}$

B.  $\stackrel{\to }{AB}.\stackrel{\to }{AC} = \stackrel{\to }{AC}.\stackrel{\to }{AD} \ne \stackrel{\to }{AB}.\stackrel{\to }{AD}$

C.  $\stackrel{\to }{AB}.\stackrel{\to }{AC} = \stackrel{\to }{AC}.\stackrel{\to }{AD} = \stackrel{\to }{AB}.\stackrel{\to }{AD}$

D.  $\stackrel{\to }{AB}.\stackrel{\to }{AC} \ne \stackrel{\to }{AC}.\stackrel{\to }{AD} \ne \stackrel{\to }{AB}.\stackrel{\to }{AD}$

Answer 1

[Cao Minh Tâm]

Ta có:  A B → . C D →   =   A C → . B D →   =   A D → . C B →   =   0

⇒ A B → ( A D →   -   A C → )   =   A C → ( A D →   -   A B →   )   =   A D → ( A B →   -   A C → )   =   0

⇒ A B → . A C →   =   A C → . A D →   =   A B → . A D →

Đáp án C