Chapter 12.1, Problem 25HP

To determine

The following statement is always, sometimes or never true is to be explain:

Three planes do not intersect in a point.

Answer to Problem 25HP

The given statement is sometimes true.

Explanation of Solution

The statement is ‘three planes do not intersect in a point’.

If three planes are perpendicular to each other then it will inersects at single point which is clearly shown by the above figure.

But in case of the following figures, the given three planes satisfy the conditions as:

1. The intersection of the three planes is a line.



2. Two coincident planes and the other intersecting them in a line



3. Each plane cuts the other two in a line



4. All three planes are parallel to each other.



5. Just two planes are parallel, and the third plane cuts each in a line

Hence, the given statement is sometimes true.

Conclusion:

Hence, the given statement is sometimes true.