📐 Mathematics · Vector Algebra · JEE

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

Answer: Perpendicular.

Correct answer: C. Perpendicular

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

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