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JEE Main202224 Jun 2022Morning ShiftMathematicsVector AlgebraActual

Let a ^ , b ^ be unit vectors. If c → be a vector such that the angle between a ^ and c → is π 12 , and b ^ = c → + 2 c → × a ^ , then 6 c → 2 is equal to:

Options

  1. A6 3 - 3
  2. B6 3 + 3
  3. C3 + 3
  4. D6 3 + 1

Correct answer

B. 6 3 + 3

Step-by-step solution

We have, b ^ = c → + 2 c → × a ^ , b ^ · b ^ = c → + 2 c → × a ^ · c → + 2 c → × a ^ ⇒ 1 = c → · c → + c → · 2 c → × a ^ + 2 c → × a ^ · c → + 4 c → × a ^ · c → × a ^ ⇒ 1 = c → 2 + 0 + 0 + c → × a ^ 2   ⇒ 1 = c → 2 + 4 c → 2 a ^ 2 sin 2 π 12 ⇒ 1 = c → 2 + 4 c → 2 1 - cos π 6 2 ⇒ 1 = c

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