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AP EAMCET201823 Apr 2018Morning ShiftMathematicsThree Dimensional GeometryActual

A plane passes through the point (3,5,7) . If the direction ratios of its normal are equal to the intercepts made by the plane x+3 y+2 z=9 with the coordinate axes, then the equation of that plane is

Options

  1. Ax + y + z = 5
  2. B6x + 2 y + 3z = 105
  3. C12 x + 4y + 6z = 49
  4. D6x + 2 y + 3z = 49

Correct answer

D. 6x + 2 y + 3z = 49

Step-by-step solution

Given equation of plane. aligned x+3 y+2 z & =9 x 9 + y 3 + z ( 9 2 ) & =1 aligned So, intercepts are 9,3, 9 2 . According to the questions, direction ratio of normal is 9,3, 9 2 and plane passes through (3,5,7) Equation of plane is aligned & & (x-3) 9+(y-5) 3+(z-7) 9 2 & =0 & & 9 x-27+3 y-15+ 9 2 z- 63 2 & =0 & & 18 x+6 y+9 z & =54+30+63 & & 18 x+6 y+9 z & =147 & & 6 x+2 y+3 z & =49 aligned

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