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JEE Main202325 Jan 2023Morning ShiftMathematicsVector AlgebraActual

The vector a → = - i ^ + 2 j ^ + k ^ is rotated through a right angle, passing through the y -axis in its way and the resulting vector is b → . Then the projection of 3 a → + 2 b → on c → = 5 i ^ + 4 j ^ + 3 k ^ is

Options

  1. A3 2
  2. B1
  3. C6
  4. D2 3

Correct answer

A. 3 2

Step-by-step solution

Given, The vector a → = - i ^ + 2 j ^ + k ^ is rotated through a right angle, passing through the y -axis in its way and the resulting vector is b → Now taking, b → = λ a → × a → × j ^ note here we have taken cross vector with j ^ as it is rotated along y - axis ⇒ b → = λ - i ^ + 2 j ^ + k ^ × - i ^ + 2 j ^ + k ^ × j ^ ⇒ b → = λ - i ^ + 2 j ^ + k ^ × - i ^ - k ^ ⇒ b → = λ i ^ j ^ k ^ - 1 2 1 - 1 0 - 1 &#86

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