We are given two planes in 3D space, defined by the following equations: Plane $\alpha$: $3x - y + 2z + 2 = 0$ Plane $\beta$: $6x - 2y + 4z + 4 = 0$ The problem asks something about the intersection of the planes. We are likely asked to determine if the planes are parallel, perpendicular, or intersecting.

1. Problem Description

We are given two planes in 3D space, defined by the following equations:

Plane $\alpha$: $3x - y + 2z + 2 = 0$

Plane $\beta$: $6x - 2y + 4z + 4 = 0$

The problem asks something about the intersection of the planes. We are likely asked to determine if the planes are parallel, perpendicular, or intersecting.

2. Solution Steps

Let's examine the equations of the planes:

Plane $\alpha$: $3x - y + 2z + 2 = 0$

Plane $\beta$: $6x - 2y + 4z + 4 = 0$

We can observe that the equation of plane $\beta$ can be obtained by multiplying the equation of plane $\alpha$ by 2:

$2(3x - y + 2z + 2) = 6x - 2y + 4z + 4 = 0$

This means the two equations represent the same plane. Therefore, the two planes are identical.

3. Final Answer

The two planes are identical.