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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Let a , b , c be three coplanar unit vectors such that a + b + c = 0 . If three vectors p , q , r parallel to a , b , c respectively and having integral but different magnitudes, then among the following options | p + q + r | can take a value equal to

Options

  1. A1
  2. B0
  3. C3
  4. D2

Correct answer

D. 2

Step-by-step solution

Let a , b , c lie in the xy plane Let a = i , b =- 1 2 i + 3 2 j and c =- 1 2 i - 3 2 j aligned & | p + q + r |=| a + b +v c |= | i + (- 1 2 i + 3 2 j )+v [- 1 2 i - 3 2 j ] | & = ( - 2 - v 2 )^2+ 3 4 ( -v)^2 = ^2+ ^2+v^2- - v- v & = 1 2 ( - )^2+( -v)^2+(v- )^2 1 2 1+1+4 = 3 aligned | p + q + r | can take a value equal to 3 and 2 .

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