Angle Between Two Planes

Step 1: Find the direction vectors of the given lines

Let the normal vectors of the given planes be:

Step 2: Find the direction vector of the line of intersection (cross product of normals)

Step 3: Equation of the plane containing the given lines and passing through point (1, 2, 3)

Using vector as the normal vector and point (1, 2, 3):

Step 4: Find the perpendicular distance from the origin to the plane

The distance from point where to the plane is:

Given that the distance is , solve:

Final Answer: Option (C): 6