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KVPY2013MathematicsVector Algebra

Let v ₁, v₂ , v₃ , v₄ be unit vectors in the x y -plane, one each in the interior of the four quadrants. Which of the following statements is necessarily true?

Options

  1. Av₁ + v₂ + v₃ + v₄ =0
  2. BThere exist i , j with 1 i < j 4 such v_ i + v_ j is in the first quadrant
  3. CThere exist i , j with 1 i < j 4 such that v _ i v_ j < 0
  4. DThere exist i, j with 1 i 0

Correct answer

A. v₁ + v₂ + v₃ + v₄ =0

Step-by-step solution

In this case B, C, D are not possible.

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