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Let a → be a vector in the x y - plane making an angle of 6 0 o with the positive x -axis and a → - i ^ is the geometric mean of a → and a → - 2 i ^ , then the value of a → is equal to

Options

  1. A2
  2. B2 + 1
  3. C2 - 1
  4. D2

Correct answer

C. 2 - 1

Step-by-step solution

Let, a → = x i ^ + 3 x j ^ Given, a → - i ^ 2 = a → a → - 2 i ^ ⇒ x - 1 2 + 3 x 2 = 2 x x - 2 2 + 3 x 2 On simplifying, we get, x = 1 2 2 - 1 ⇒ a → = 2 - 1

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