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JEE Main2018MathematicsVector AlgebraActual

If a → , b → , c → are unit vectors such that a → + 2 b → + 2 c → = 0 → , then a → × c → is equal to :

Options

  1. A1 4
  2. B15 16
  3. C15 4
  4. D15 16

Correct answer

C. 15 4

Step-by-step solution

Given a → + 2 b → + 2 c → = 0 ⇒ a → + 2 c → = - 2 b → Squaring both sides, ⇒ a → 2 + 4 c → 2 + 4 a → . c → = 4 b → 2 ⇒ 1 + 4 + 4 cos ⁡ θ = 4 ⇒ cos ⁡ θ = - 1 4 ∴ sin ⁡ θ = 1 - cos 2 ⁡ θ = 15 4 Now, a → × c → = a → c → sin ⁡ θ = 15 4

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