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JEE Main202225 Jul 2022Evening ShiftMathematicsVector AlgebraActual

Let a → = i ^ - j ^ + 2 k ^ and let b → be a vector such that a → × b → = 2 i ^ - k ^ and a → · b → = 3 . Then the projection of b → on the vector a → - b → is:

Options

  1. A2 21
  2. B2 3 7
  3. C2 3 7 3
  4. D2 3

Correct answer

A. 2 21

Step-by-step solution

Given, a → = i ^ - j ^ + 2 k ^ , a → × b → = 2 i ^ - k ^ and a → · b → = 3 Now using the formula a → × b → 2 + a → · b → 2 = a → 2 · b → 2 sin 2 θ + a → 2 · b → 2 cos 2 θ ⇒ a → × b → 2 + a → · b → 2 = a → 2 · b → 2 sin 2 θ + cos 2 θ = a → 2 · b → 2 We get, ⇒ 2 i ^ - k ^ 2 + 3 2 = i ^ - j ^ + 2 k ^ 2 b → 2

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