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AP EAMCET2015MathematicsThree Dimensional Geometry

The length of perpendicular from the origin to the plane which makes intercepts 1 3 , 1 4 and 1 5 respectively on the coordinate axes is

Options

  1. A1 5 2
  2. B1 10
  3. C5 2
  4. D5

Correct answer

A. 1 5 2

Step-by-step solution

Here, intercepts made with the coordinate axes X , Y and Z are 1 3 , 1 4 and 1 5 respectively. Intercept form of a plane is x a + y b + z c =1 We have, a= 1 3 , b= 1 4 , c= 1 5 Equation of plane is aligned & 3 x+4 y+5 z=1 & 3 x+4 y+5 z-1=0 aligned Distance from origin = | 3 0+4 0+5 0-1 3^2+4^2+5^2 |= 1 5 2

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