how many lines are determined by the given condition,?

Question

three planes, each of which intersects the other at different places

Answer 1

3

OK, in order to not have a point where all 3 planes intersect imagine this. Take the first two planes and intersect them to form a line. They have to form a line, otherwise, they either coincide or don't intersect.

Now, how do you place the 3rd plane so that it doesn't touch the line. Because, if it touches the line, you will violate the requirement that they all intersect each other at different places.

The only way to place the 3rd plane to do this is to form another line in each of the other planes that is parallel to the first line formed. This means forming exactly 3 lines all of which are parallel to one another in the planes in which they lie.

Answer 2

If there is no point where the three planes intersect then the planes must form three lines. Two planes to each line.

Answer 3

3
If you have 3 planes, P1, P2, and P3, and every plane intersectects every other plane, there is a line defined by each intersection.
The intersections are P1 intersect P2, P2 intersect P3 and P3 intersect P1. Since the intersections are at different places, the precludes the case where they all intersect along the same line.

Answer 4

Suppose you have plane A, B and C
When A intersects B, it determines one line....l1
When A intersects C, it determines one line....l2
When B and C intersect, they determine .......l3
So ....3 lines....is your answer,

Answer 5

Three lines that intersect to form a triangle.

Answer 6

3 lines would be formed

Answer 7

Three 0nly

Answer 8

Could you diagram that?

That was a smartass answer. But come to think of it, if you *did* diagram it, then you'd have your answer, wouldn't you?