Find the equation of the plane through the intersection of the pla | Filo
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Class 12

Math

3D Geometry

Three Dimensional Geometry

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Find the equation of the plane through the intersection of the planes and and parallel to the line

Solution: The equation of the plane passing through the intersection of the given planes is
 
                   ----- ( 1 )
The given line is
Dividing this equation by , we get
 
The direction ratios of this line are proportional to
So, the normal to the plane is perpendicular to the line whose direction are proportional to
 
 
 
 
 
Substituting this equation ( 1 ), we get
 

 

 
Multiplying both sides by we get,
 
 

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