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📐 Mathematics  ·  Vector Algebra  ·  JEE

If |a| = 3, |b| = 4 and |a + b| = 5, then a·b equals:

Answer: 0.

  • A 0
  • B 6
  • C 12
  • D −12

Correct answer: A. 0

Explanation: |a + b|² = |a|² + |b|² + 2a·b gives 25 = 9 + 16 + 2a·b, so a·b = 0.

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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