Answer: b - c is parallel to a.
- A b = c
- B b - c is perpendicular to a
- C b - c is parallel to a
- D b + c = 0
Correct answer: C. b - c is parallel to a
Explanation: a×b = a×c → a×(b−c) = 0. Cross product is zero iff vectors are parallel (or one is zero). So (b−c) is parallel to a. Note: b−c need not be zero, so b≠c in general. Answer: b−c is parallel to a.
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