Chapter 12.1, Problem 24HP

To determine

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

Two planes intersect in a single point.

Answer to Problem 24HP

The given statement is never true.

The two planes intersects along a line.

Explanation of Solution

The statement is ‘two planes intersect in a single point’.

Two distinct planes which are either parallel or intersects each other along line never has a single point as an intersection point.

Because only lines intersects a a point, and planes are not lines.

So, the two planes intersects along a line or two points; not a single point.

Hence, the given statement is never true.

Conclusion:

Hence, the two planes intersects along a line.