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JEE Main202227 Jun 2022Morning ShiftMathematicsVector AlgebraActual

Let a → = i ^ + j ^ - k ^ and c → = 2 i ^ - 3 j ^ + 2 k ^ . Then the number of vectors b → such that b → × c → = a → and b → ∈ 1 , 2 , … , 10 is

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

A. 0

Step-by-step solution

Given, a → = i + j - k and c → = 2 i - 3 j + 2 k b → × c → = a → and b → ∈ 1 , 2 … … 10 ∵   b → × c → = a → ⇒   a → is perpendicular to b → as well as a → is perpendicular to c → , so a → · c → = 0 as they are perpendicular. Now checking a → · c → = 2 - 3 - 2 = - 3 ≠ 0 This b → × c → = a → is not possible. So, number of vectors

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