Q14 - Geometry

Question

State whether it is possible for the figure described to exist. Write yes or no.

Three points all lie in each of the two planes.

Step-by-Step Solution

Answer

Yes, it is possible that three points all lie in each of the two planes.

Step 1. Write the concept involved.

The concept involved is that if there are three collinear points then through these points infinite planes can pass but if there are three non-collinear points then through these points only one plane can pass.

Step 2. Draw the diagram of two planes passing through three points A, B, and C.

The figure representing two planes passing through three points A, B, and C is:

Step 3. State whether it is possible that three points all lie in each of two planes by considering the concept and above diagram.

From the diagram and concept, it can be noticed that if three points are collinear then all three points can lie in each of the two planes. Therefore, it is possible that any three points can simultaneously lie on the two different planes.

Therefore, it is possible that three points all lie in each of the two planes.