question_answer

A tetrahedron has vertices at O(0, 0, 0), A(1, 2, 3), B(2, 1, 3) and C(-1, 1, 2). Then, the angle between the faces OAB and ABC will be     AIEEE  Solved  Paper-2003

A) \[{{\cos }^{-1}}\left( \frac{19}{35} \right)\]       

B)       \[{{\cos }^{-1}}\left( \frac{17}{31} \right)\]                          

C) \[{{30}^{o}}\]                                    

D) \[{{90}^{o}}\]

Correct Answer: A

Solution :

If  and  inclined at an angle , then     Vector perpendicular to face                 Vector perpendicular to face Since, angle between faces equals angle between their normals. Therefore.