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It is found that |A + B| = |A|. This necessarily implies,

  1. B = 0
  2. A, B are antiparallel
  3. A, B are perpendicular
  4. A ⋅ B ≤ 0 

Answer (Detailed Solution Below)

Option 4 : A ⋅ B ≤ 0 

Detailed Solution

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Solution: 

|A + B| = |A|

Squaring both the sides

|A+B|2 = |A|2

|A|2 + |B|2 + 2.|A| |B| cosθ  = |A|2 

∴ |B|2 + 2.|A| |B| cosθ = 0

2.|A| |B| cosθ = - |B|2 

|A| |B| cosθ = 

A.B = 

∴ A.B  0 {A.B = 0 when B = 0}

Hence, the correct option is (4)

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