EQUATION OF THE PLANE IN 3 DIMENSIONS

[henrry]

EQUATION OF THE PLANE IN 3 DIMENSIONS
The best way to overcome Calculus 3 problem is to try many exercises or problems and I always try to solve many times until I get the correct answer. The funny thing is, sometimes I just get stuck during the process of solving the problems and I indeed encounter the following difficulty, so I need your assistance to solve the following problem:
Find the equation of the plane that passes through the line of intersections of the planes x - z=1 and y + 2z=3 and is perpendicular to the plane x + y-2z=1
Note that you don’t have to be perfect so try your best to send me any possible best solution
Thanks

 

[pka]

EQUATION OF THE PLANE IN 3 DIMENSIONS
Find the equation of the plane that passes through the line of intersections of the planes x - z=1 and y + 2z=3 and is perpendicular to the plane x + y-2z=1
Note that you don’t have to be perfect so try your best to send me any possible best solution
Thanks

Find two points \(\displaystyle P~\&~Q\) on the line of intersection.
The needed normal is \(\displaystyle \overrightarrow {PQ}\times <1,1,-2>\).