Final answer:
Two planes that intersect in line BC can be described as Plane ABC, defined by points A, B, and C, and Plane BCD, defined by points B, C, and D. Both planes share line BC, making it their line of intersection. Points A, B, C, and D are noncoplanar, confirming the existence of two distinct intersecting planes.
Step-by-step explanation:
To describe two planes that intersect in line BC, we can think of each plane as being defined by three points. Because we know that points A, B, and C are noncollinear and points B, C, and D are noncollinear, we can use these points to define the two planes.
Let's call the first plane Plane ABC which is defined by points A, B, and C. Since these three points are noncollinear, they define a unique plane. Similarly, we can define another plane, Plane BCD, using points B, C, and D. Plane BCD is unique because these points are also noncollinear. Since both planes contain the line BC (the line formed by points B and C), they will intersect along this line, creating a line of intersection which is the common line BC.
Thus, the two planes Plane ABC and Plane BCD intersect along line BC. It's important to note that the four points A, B, C, and D are noncoplanar, which means no single plane can contain all four points. This fact ensures that there are indeed two distinct planes as described.