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JEE MainMathematicsThree Dimensional Geometry

Let a line L pass through the origin and be parallel to the line of intersection of the planes x + y - z = 1 and x - y + z = 2 . If the perpendicular distance from the point P( , 2, 4) to the line L is 6 , then the value of ^2 is:

Options

  1. A4
  2. B2
  3. C8
  4. D34

Correct answer

A. 4

Step-by-step solution

The direction vector of the line of intersection of the given planes is parallel to the cross product of their normal vectors. d = vmatrix i & j & k 1 & 1 & -1 1 & -1 & 1 vmatrix = 0 i - 2 j - 2 k So, the direction ratios of the line L are (0, 1, 1) . Since L passes through the origin, its equation is r = ( j + k ) . A general point on L is F(0, , ) . The vector PF from P( , 2, 4) to F is (- , - 2, - 4) . Since PF is perpendicular to L , we have PF (0, 1, 1) = 0 0(- ) + 1( - 2) + 1( - 4) = 0 2 - 6 = 0 = 3 Thus, the

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