Question

How many planes can be made to pass through three distinct points?
$
  A{\text{ One if they are collinear}} \\
  {\text{B Infinite if they are collinear}} \\
  {\text{C Only one if they are non - collinear}} \\
  {\text{D Both B and C}} \\
 $

Answer 1

Hint- Here we will use two concepts of planes passing through three points for both the collinear and non-collinear points as the question does not define the particular points.

Complete step-by-step solution -
We know that only one plane can pass through three non-collinear points.
And if a line intersects a plane that doesn’t contain the line, then the intersection is exactly one point.
For collinear points-
If two different planes intersect, then their intersection is a line.
Also if a line and a plane have no points in common, then they are parallel.
As if a plane intersects two parallel planes, then the lines of intersection are parallel.
Therefore, an infinite number of planes can be made to pass through three collinear points.
So from above we conclude that B and C are true.
$\therefore $ Option D is right.

Note- In order to solve this type of question, we must know the concept of planes passing through three points where points may be collinear or non-collinear. Also we must know about the planes passing through two collinear or non-collinear points.