Final answer:
To find an equation of a plane orthogonal to two given planes in Cartesian coordinate system, find a normal vector to the desired plane. The equation of the desired plane will be y = c, where c is a constant.
Step-by-step explanation:
To find an equation of a plane that is orthogonal to two given planes in Cartesian coordinate system, we need to find a normal vector to the desired plane. The normal vector of a plane is perpendicular to the plane's surface. Since the given planes are parallel to the x-axis, any vector with x-axis component equal to zero will be normal to them. Therefore, a possible normal vector to the desired plane could be (0, 1, 0). This means that the equation of the desired plane will have the form: y = c, where c is a constant.
For example, if we want the plane to pass through the point (1, 2, 3), the equation of the plane would be y = 2. This equation represents a plane that is orthogonal to the given planes and passes through the point (1, 2, 3).