InterviewSolution
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InterviewSolution
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Find the equations of the planes parallel to the plane `x-2y+2z-3=0`which is at a unit distance from the point `(1,2,3)dot` |
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Answer» The equation fo the given plane is `x-2y+2z-3=0`. Let the required plane parallel to the given plane be `x-2y+2z+lambda=0` for some real number `lambda`…………….(i) Now, the plane (i) is at unit distance from the point (1,2,3). `therefore (|1-(2xx2)+(2xx3)+lambda|)/(1^(2)+(-2)^(2)+2^(2)) = 1 rArr |lambda+3|=3`. `rArr lambda+3=3` or `-(lambda+3)=3`. `rArr lambda=0` or `lambda=-6`. Hence, the equations of the required planes are `x-2y+2z=0` and `x-2y+2z-6=0`. |
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