Final answer:
The equation of the plane parallel to the plane 2x + y + z = 7 and that passes through the point (1, -1, 3) is 2x + y + z = 4.
Step-by-step explanation:
To find the equation of a plane that is parallel to a given plane, we must understand that parallel planes have the same normal vector. The given plane is 2x + y + z = 7. Since our plane needs to be parallel to the given one, it will share the same coefficients for x, y, and z.
Therefore, the general form of our plane will also be 2x + y + z = D, where D is a constant that we need to determine. Using the point (1, -1, 3) which lies on our plane, we substitute these values into the equation to find D:
- 2(1) + (-1) + (3) = D
- 2 - 1 + 3 = D
- 4 = D
Now we can write the equation of our plane as 2x + y + z = 4.