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AP EAMCET2013MathematicsThree Dimensional Geometry

A plane passing through (-1,2,3) and whose normal makes equal angles with the coordinate axes is

Options

  1. Ax+y+z+4=0
  2. Bx-y+z+4=0
  3. Cx+y+z-4=0
  4. Dx+y+z=0

Correct answer

C. x+y+z-4=0

Step-by-step solution

A plane passing through the point (-1,2,3) , then its equation is a(x+1)+b(y-2)+c(z-3)=0 where a, b, c are direction ratios of normal to the plane A B C . So, the normal makes equal angles with coordinate axes i.e., (a, b, c)= ( 1 3 , 1 3 , 1 3 ) Now, from Eq. (i), array cc 1 3 (x+1)+ 1 3 (y-2)+ 1 3 (z-3)=0 x+y+z-4 & =0 array

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