Find the equation of a plane given a point and a parallel plane?

Please describe in detail how to solve for this equation! Thank you an advance!





Find the equation of the plane that passes through the point (-1, 6, -5) and is parallel to the plane x+y+z+2=0.





I know parallel planes have the same normal vector, but what procedure do I use to solve this?|||The normal vector of the given plane is n = i + j + k.





So your normal vector for the plane through your point must be n or some nonzero multiple of n.





A plane with this normal vector through the point (-1,6,-5) has the formula





n_x(x - x_0) + n_y(y - y_0) + n_z(z - z_0) = 0





Where the notation n_x means the x component of the normal vector and x_0 is the given x coordinate (-1 in this case). Same for _y and _z.





(x + 1) + (y - 6) + (z + 5) = 0





Simplify by adding like terms.





x + y + z = 0