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📐 Mathematics  ·  Vector Algebra  ·  JEE

If a, b, c are mutually perpendicular unit vectors, |a + b + c|<sup>2</sup> =

Answer: 3.

  • A 3
  • B 1
  • C sqrt(3)
  • D 9

Correct answer: A. 3

Explanation: Expand: |a+b+c|² = |a|²+|b|²+|c|²+2(a·b+b·c+c·a). Unit vectors: |a|²=|b|²=|c|²=1. Mutually perpendicular: all dot products = 0. So |a+b+c|² = 1+1+1+0 = 3. Answer: 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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