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JEE Math Practice Question

Let p be the plane passing through the intersection of the planes $$\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 5$$ and $$\overrightarrow r \,.\,\left( {2\widehat i - \widehat j + \widehat k} \right) = 3$$, and the point (2, 1, $$-$$2). Let the position vectors of the points X and Y be $$\widehat i - 2\widehat j + 4\widehat k$$ and $$5\widehat i - \widehat j + 2\widehat k$$ respectively. Then the points :

  1. A.X and X + Y are on the same side of P
  2. B.Y and Y $$-$$ X are on the opposite sides of P
  3. C.X and Y are on the opposite sides of P
  4. D.X + Y and X $$-$$ Y are on the same side of P

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