Answer: (p + q)/2.
- A (p + q)/2
- B p + q
- C p - q
- D (p - q)/2
Correct answer: A. (p + q)/2
Explanation: Setting up: p = AB + BC = AB + AD and q = -AB + AD. Adding: p + q = 2AD so AD = (p+q)/2. Subtracting: p - q = 2AB so AB = (p-q)/2. Wait: q = BD = BA + AD = -AB + AD. So p+q = 2AD and p-q = 2AB. Thus AB = (p-q)/2. Answer is index 3.
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