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Two points P and Q are lying on the curve y = l o g 2 x + 3 in x y plane such that O P → ⋅ i ^ = 1 and O Q → ⋅ j ^ = 3 , then the value of O Q → - 2 O P → is (where, O is the origin)

Options

  1. A6
  2. B7
  3. C8
  4. D10

Correct answer

D. 10

Step-by-step solution

Let P x 1 , l o g 2 x 1 + 3 and Q x 2 , l o g 2 x 2 + 3 ∵ O P → ⋅ i ^ = 1 ⇒ x 1 = 1 ⇒ P ( 1,2 ) ∵ O Q → ⋅ j ^ = 3 ⇒ l o g 2 x 2 + 3 = 3 ⇒ x 2 = 5 ⇒ Q 5,3 O Q → - 2 O P → = 5 i ^ + 3 j ^ - 2 i ^ + 2 j ^ = 3 i ^ - j ^ = 10

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