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JEE Main2014MathematicsVector AlgebraActual

If x , y and z are three unit vectors in threedimensional space, then the minimum value of | x + y |^2+| y + z |^2+| z + x |^2

Options

  1. A3 2
  2. B3
  3. C3 3
  4. D6

Correct answer

B. 3

Step-by-step solution

( x + y + z )^2 0 aligned & 3+2 x y 0 & 2 x y -3 aligned Now, | x + y |^2+| y + z |^2+| z + x |^2=6+2 x . y 6+(-3) | x + y |^2+| y + z |^2+| z + x |^2 3

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