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JEE Main20208 Jan 2020Evening ShiftMathematicsVector AlgebraActual

Let a → = i ^ - 2 j ^ + k ^ and b → = i ^ - j ^ + k ^ , be two vectors. If c → , is a vector such that b → × c → = b → × a → and c → ⋅ a → = 0 , then c → ⋅ b → , is equal to.

Options

  1. A- 3 2
  2. B1 2
  3. C- 1 2
  4. D- 1

Correct answer

C. - 1 2

Step-by-step solution

a → × b → × c → = a → × b → × a → ⇒ - a → . b → c → = a → . a → b → - a → . b → a → Using given information a → = i ^ - 2 j ^ + k ^ and b → = i ^ - j ^ + k ^ , we can write a → . b → = 4 , a → . a → = 6 ⇒ - 4 c → = 6 i ^ - j ^ + k ^ - 4 i ^ - 2 j ^ + k ^ ⇒ - 4 c → = 2 i ^ + 2 j ^ + 2 k ^ ⇒ c → = - 1 2 i ^ + j ^ + k ^ ⇒ b &#8

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