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Let a line L be the line of intersection of the planes x + y - z = 1 and 2x - y + z = 2 . The perpendicular distance of the point Q(3, 4, 2) from the line L is

Options

  1. A6
  2. B2 5
  3. C2 6
  4. D14

Correct answer

A. 6

Step-by-step solution

The direction ratios of the line of intersection L are given by the cross product of the normal vectors of the two planes. b = vmatrix i & j & k 1 & 1 & -1 2 & -1 & 1 vmatrix = i (1 - 1) - j (1 - (-2)) + k (-1 - 2) = (0, -3, -3) We can take the direction ratios of L as (0, 1, 1) . To find a point on L , let x = 1 . Substituting this into the plane equations gives 1 + y - z = 1 y = z and 2 - y + z = 2 y = z . Choosing y = 0 , we get z = 0 . Thus, (1, 0, 0) is a point on L . The equation of the line L is r = (1, 0, 0

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