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JEE Main202313 Apr 2023Evening ShiftMathematicsVector AlgebraActual

Let | a → | = 2 , | b → | = 3 and the angle between the vectors a → and b → be π 4 . Then | ( a → + 2 b → ) × ( 2 a → - 3 b → ) | 2 is equal to

Options

  1. A441
  2. B482
  3. C841
  4. D882

Correct answer

D. 882

Step-by-step solution

Given, | a → | = 2 , | b → | = 3 and the angle between the vectors a → and b → be π 4 , Now solving, | ( a → + 2 b → ) × ( 2 a → - 3 b → ) | 2 = | - 3 ( a → × b → ) + 4 ( b → × a → ) | 2 as   a → × a → = 0   &   b → × b → = 0 = | 7 ( b → × a → ) | 2 as   b → × a → = - a → × b → = 49 | a | 2 | b | 2 sin 2 π 4 = 49

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