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Let P and Q are two points in the x y plane on the curve y = x 11 – 2 x 7 + 7 x 3 + 11 x + 6 such that O P → ⋅ i ^ = 5 , O Q → ⋅ i ^ = - 5 , then the magnitude of O P → + O Q → is

Options

  1. A10
  2. B12
  3. C14
  4. D8

Correct answer

B. 12

Step-by-step solution

Let P and Q be x 1 , y 1 and x 2 , y 2 O P → ⋅ i ^ = 5 ⇒ x 1 = 5 O Q → ⋅ i ^ = - 5 ⇒ x 2 = - 5 Let y = f x = x 11 - 2 x 7 + 7 x 3 + 11 x + 6 ∴ y 1 = f x 1 = f 5 y 2 = f x 2 = f - 5 O P → + O Q → = x 1 + x 2 i ^ + y 1 + y 2 j ^ = f 5 + f - 5 j ^ = 12 j ^ O P → + O Q → = 1 2

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