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📐 Mathematics  ·  Vector Algebra  ·  JEE

If |a + b| = |a - b|, then a and b must be:

Answer: Perpendicular.

  • A Parallel
  • B Equal in magnitude
  • C Perpendicular
  • D Collinear

Correct answer: C. Perpendicular

Explanation: |a+b|<sup>2</sup> = |a-b|<sup>2</sup> gives |a|<sup>2</sup>+2a.b+|b|<sup>2</sup> = |a|<sup>2</sup>-2a.b+|b|<sup>2</sup>, so 4a.b = 0. Hence a.b = 0, meaning they are perpendicular.

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

Read the full Vector Algebra notes →