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JEE Main202324 Jan 2023Morning ShiftMathematicsVector AlgebraActual

Let u → = i ^ - j ^ - 2 k ^ , v → = 2 i ^ + j ^ - k ^ , v → · w → = 2 and v → × w → = u → + λ v → , then u → · w → is equal to

Options

  1. A1
  2. B3 2
  3. C2
  4. D- 2 3

Correct answer

A. 1

Step-by-step solution

Given: v → × w → = u → + λ v →       . . . . 1 Taking dot product with w → , we get w → · v → × w → = w → · u → + λ w → · v → ⇒ u → · w → + λ w → · v → = 0 ⇒ u → · w → = - 2 λ       . . . . 2 Taking dot product with v → in 1 , we get v → · v → × w → = v → · u &#859

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