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JEE Main202227 Jun 2022Evening ShiftMathematicsVector AlgebraActual

Let a → and b → be the vectors along the diagonal of a parallelogram having area 2 2 . Let the angle between a → and b → be acute. a → = 1 and a → . b → = a → × b → . If c → = 2 2 a → × b → - 2 b → , then an angle between b → and c → is

Options

  1. A- π 4
  2. B5 π 6
  3. Cπ 3
  4. D3 π 4

Correct answer

D. 3 π 4

Step-by-step solution

Area = 1 2 | a b |=2 2 | a b |=4 2 | a |=1 and | a b |=| a b | = = 4 | a b |=4 2 | a || b | 4 =4 2 | b |=8 Now, c =2 2 ( a b )-2 b | c |= (2 2 )^2| a b |^2+(2 b )^2 =16 2 Now, b c =-2| b |^2 8 16 2 =-2.64 =- 1 2 = 3 4

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