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AP EAMCET2004MathematicsThree Dimensional Geometry

If (2,-1,3) is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

Options

  1. A2 x+y-3 z+6=0
  2. B2 x-y+3 z-14=0
  3. C2 x-y+3 z-13=0
  4. D2 x+y+3 z-10=0

Correct answer

B. 2 x-y+3 z-14=0

Step-by-step solution

Where a, b, c are the direction ratios. Since, point O(0,0,0 , ) is perpendicular to the foot of the plane at a point P(2,-1,3) . Direction's of O P=2,-1,3 Since the line O P is perpendicular to the plane, therefore the direction's of the normal to the plane is proportional to the direction is of O P Required equation of plane is array rlrl & 2(x-2)-1(y+1)+3(z-3) & =0 & 2 x-y+3 z-14 =0 array

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