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Let V 1 → = i ^ + a j ^ + k ^ , V 2 → = j ^ + a k ^ and V 3 → = a i ^ + k ^ ,   ∀ a > 0 . If V 1 →   V 2 →   V 3 → is minimum, then the value of a is

Options

  1. A3
  2. B3
  3. C1 3
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

V 1 →   V 2 →   V 3 → = 1 a 1 0 1 a a 0 1 = a 3 - a + 1 = f a (say) So, for minima f ' a = 3 a 2 − 1 = 0 Hence, for minima a = 1 3   a > 0

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