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If two points P and Q are on the curve y = 2 x + 2 , such that O P → ⋅ i ^ = − 1 and O Q → ⋅ i ^ = 2 , where i ^ is a unit vector along the x -axis, then O Q → - 4 O P → is equal to

Correct answer

10

Step-by-step solution

Let P x 1 , y 1 and Q x 2 , y 2 be two points on y = 2 x + 2 ∵ O P → ⋅ i ^ = − 1 ⇒ x 1 = − 1 and y 1 = 2 O Q → ⋅ i ^ = 2 ⇒ x 2 = 2 and y 2 = 16 ⇒ O P → = - i ^ + 2 j ^ and O Q → = 2 i ^ + 16 j ^ ⇒ O Q → - 4 O P → = 6 i ^ + 8 j ^ ⇒ O Q → - 4 O P → = 10

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