Answer: [a b c] = -[b a c] but [a b c] = [b c a].
- A [a b c] = [a c b] (any swap is allowed)
- B [a b c] = -[b a c] but [a b c] = [b c a]
- C [a b c] = |a||b||c|, treating it as a simple magnitude product
- D [a b c] = (a x b).c = a.(b x c), a relation said to require coplanar vectors specifically
Correct answer: B. [a b c] = -[b a c] but [a b c] = [b c a]
Explanation: [abc] is cyclic: [abc]=[bca]=[cab]. Swapping any two adjacent vectors negates it: [abc]=-[bac]. Statement B captures both properties correctly.
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