Answer: (1/6)|[a b c]|.
- A |[a b c]|
- B (1/3)|[a b c]|
- C (1/2)|[a b c]|
- D (1/6)|[a b c]|
Correct answer: D. (1/6)|[a b c]|
Explanation: Volume of tetrahedron = (1/6)|a.(b x c)|. The parallelepiped formed by the same edges has volume |[abc]|, and the tetrahedron is 1/6 of that.
Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.
Concept context
Vectors, dot product, cross product, and geometric applications