Find an equation of the plane through the point (1, -1, -1) and parallel to the
plane $5{x} – {y} – {z} = 6$
I was shown an example of this problem but it was in a problem where it had to be perpendicular to a plane. I read carefully through this section of the book but I'm not sure how to approach this problem. I know that two planes are parallel if their norms are multiples of one another but I'm not sure how to use that idea to solve this problem, maybe my brain isn't creative enough. I also couldn't understand the solutions for other similar questions online, they weren't explained with 100% clarity. thanks.
Best Answer
It's $5x-y-z+d=0$ and substitute $(x,y,z)=(1,-1,-1)$.
I got $d=-7$ and the answer is $5x-y-z-7=0$.