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AP EAMCET20224 Jul 2022Evening ShiftMathematicsVector AlgebraActual

If P , Q are two points on the curve y = 2 x + 2 in the rectangular Cartesian coordinate system such that O P ¯ · i ^ = - 1 , O Q ¯ · i ^ = 2 then O Q ¯ - 4 O P ¯ =

Options

  1. A3 i ¯ + 8 j ¯
  2. B4 i ¯ + 6 j ¯
  3. C6 i ¯ + 8 j ¯
  4. D4 i ¯ + 3 j ¯

Correct answer

C. 6 i ¯ + 8 j ¯

Step-by-step solution

Given, O P ¯ . . i ^ = - 1 ⇒ P x = - 1 P lies on y = 2 x + 2 ⇒ y = 2 - 1 + 2 ⇒ y = 2 So, P x , P y = - 1 , 2 Now O Q ¯ · i ^ = 2 ⇒ Q x = 2 Also Q lies on y = 2 x + 2 ⇒ y = 2 2 + 2 ⇒ y = 16 So, Q x , Q y = 2 , 16 Now O Q ¯ = 2 i + 16 j And O P ¯ = - i + 2 j So, O Q ¯ - 4 O P ¯ = 2 i + 16 j + 4 i - 8 j = 6 i + 8 j

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