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JEE Main2017MathematicsVector AlgebraActual

Given, a → = 2 i ^ + j ^ - 2 k ^ and b → = i ^ + j ^ . Let c → be a vector such that c → - a → = 3 , a → × b → × c → = 3 and the angle between c → and a → × b → be 30 ° . Then a → ⋅ c → is equal to:

Options

  1. A25 8
  2. B2
  3. C5
  4. D1 8

Correct answer

B. 2

Step-by-step solution

Given, a → = 2 i ^ + j ^ - 2 k ^ b → = i ^ + j ^ Now, a → × b → = i ^ j ^ k ^ 2 1 - 2 1 1 0 ⇒ a → × b → = 2 i ^ - 2 j ^ + k ^ ⇒ a → × b → = 3 Given, a → × b → × c → = 3 ⇒ a → × b → c → sin 30 ° = 3 ⇒ c → = 2 Now, c → - a → = 3 ⇒ c → - a → 2 = 9 ⇒ c → 2 + a → 2 - 2 a → · c → = 9 ⇒ a → . c &#859

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