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📐 Mathematics  ·  Vector Algebra  ·  JEE

If ABCD is a parallelogram with diagonal AC = p and BD = q, then AB =

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.

xya (4,1)b (2,3)a + b (6,4)

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

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