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JEE Advanced2013MathematicsThree Dimensional GeometryActual

Consider the lines L ⁡ 1 : x - 1 2 = y - 1 = z + 3 1 , L ⁡ 2 : x - 4 1 = y + 3 1 = z + 3 2 and the planes P ⁡ 1 : 7 x + y + 2 z = 3 , P ⁡ 2 : 3 x + 5 y - 6 z = 4 . Let a x + b y + c z = d ⁡ be the equation of the plane passing through the point of intersection of L 1 and L 2 , and perpendicular to planes P 1 and P 2 . Match List- I with List - II and select the correct answer using the c

Options

  1. Aa-r;b-q;c-s;d-p;
  2. Ba-q;b-p;c-r;d-s;
  3. Ca-s;b-p;c-r;d-q;
  4. Da-r;b-q;c-p;d-s;

Correct answer

A. a-r;b-q;c-s;d-p;

Step-by-step solution

Given equation of two line L 1 and L 2 L 1 : x - 1 2 = y - 1 = z + 3 1 = k 1   s a y L 2       :   x - 4 1 = y + 3 1   = z + 3 2 = k 2     s a y And equation of two planes P 1 and P 2 P 1 :  7 x + y + 2 z = 3 , P 2 :  3 x + 5 y - 6 z = 4 . Evaluating unit vector n ^ perpendicular to both the given planes P 1 and P 2 ⇒ n → = i ^ j ^ k ^ 7 1 2 3 5 - 6 = i ^ - 6 . 1 - 2 . 5 - j ^ - 6 . 7 - 2 . 3 + k ^ 5 . 7 - 3 . 1 = - 6 - 10 i ^ - - 42 - 6 j ^ + 35 - 3 k ^

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