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AP EAMCET2011MathematicsThree Dimensional Geometry

A plane passes through (2,3,-1) and is perpendicular to the line having direction ratios 3,-4,7 . The perpendicular distance from the origin to this plane is

Options

  1. A3 74
  2. B5 74
  3. C6 74
  4. D13 74

Correct answer

D. 13 74

Step-by-step solution

The equation of the plane passes through the point (2,3,-1) is where a, b, c are the direction ratio of the normal to the plane. Also, given the plane is perpendicular to the line whose direction ratio is (3,-4,7) . So, that line and the normal of the plane are parallel. array lc & a 3 = b -4 = c 7 =k & a=3 k, b=-4 k, c=7 k array From Eq. (i) 3 k(x-2)-4 k(y-3)+7 k(z+1)=0 Now, perpendicular distance from the origin to this plane aligned & = |3 0-4 0+7 0+13| 9+16+49 & = 13 74 aligned

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