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Let a → ,   b → and c → be three vectors such that a → = 2 ,   b → = 4 ,   c → = 1 and b → × c → = 15 . If b → = 2 c → + λ a → , then the value of λ is equal to (here, the angle between b → and c → is acute)

Options

  1. A± 2
  2. B± 1
  3. C± 2 2
  4. D± 4

Correct answer

C. ± 2 2

Step-by-step solution

b → - 2 c → = λ a → ⇒ b → - 2 c → 2 = λ a → 2 ⇒ b → 2 + 4 c → 2 - 4 b → . c → = λ 2 2 ⇒ 16 + 4 - 4 b → . c → = 2 λ 2 ⇒ λ 2 = 10 - 2 b → . c →   . . .   1 Now, b → × c → 2 + b → . c → 2 = b → 2 c → 2 15 + b → . c → 2 = 16 ⇒ b → . c → = ± 1 The angle between b → and c → is acute Hence, b &#

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