Answer: Unique linear combination r = xa + yb + zc.
- A A unique scalar multiple of vector a alone, ignoring b and c
- B A representation using the vector triple product r = a x b x c
- C Unique linear combination r = xa + yb + zc
- D A simple sum of all three basis vectors, r = a + b + c
Correct answer: C. Unique linear combination r = xa + yb + zc
Explanation: Three non-coplanar (linearly independent) vectors span ℝ³ and form a basis. By the definition of a basis, every vector r has a unique representation r = xa + yb + zc where x, y, z are scalars. Answer: unique linear combination r = xa + yb + zc.
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