Answer :

Given :


Equation of plane : :


Equation of a line :



To Prove : Given line is parallel to the given plane.


Comparing given plane i.e.



with , we get,



This is the vector perpendicular to the given plane.


Now, comparing the given the equation of line i.e.



with , we get,



Now,




= 1 – 5 + 4


= 0



Therefore, a vector normal to the plane is perpendicular to the vector parallel to the line.


Hence, the given line is parallel to the given plane.


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