A tetrahedron has vertices O(0,0,0) A(1,2,1) B(2,1,3) C(-1,1,2) . Then the angle between the faces O A B and A B C will be

Step-by-step solution

To determine the angle between the faces of the tetrahedron with vertices O(0,0,0) , A(1,2,1) , B(2,1,3) , and C(-1,1,2) , the normal vectors to each face are computed using the cross product. The normal vector n₁ to face OAB is given by OA OB , where OA = (1,2,1) and OB = (2,1,3) . This yields n₁ = (5, -1, -3) . Similarly, the normal vector n₂ to face ABC is found from AB AC , with AB = (1, -1, 2) and AC = (-2, -1, 1) . The result is n₂ = (1, -5, -3) . The angle between the faces is the angle between their normals