Are These Geometry Statements True or False?

[PsychonautQQ]

Homework Statement

I only get one chance at getting these ALL right... Nazi teacher :P lol

1. Two planes parallel to a third plane are parallel.
True, planes take up a lot of space so this seems reasonable :P

2. Two lines either intersect or are parallel.
False, there is a lot of space for both of them i think

3. Two planes perpendicular to a third plane are parallel.
True Normal vectors perpendicular to a plane are parallel so I suspect this to be true


4. Two planes perpendicular to a line are parallel.
True, in my head I'm picturing a line on the xy axis. all the planes coming off of it are parallel.

5. A plane and a line either intersect or are parallel.
False, I'm imaging a line that is bound to the xy axis and a plane going past it without touching it.


6. Two lines perpendicular to a plane are parallel
True, picturing this in my head I believe they would have to be

7. Two planes either intersect or are parallel.
True, Planes are big and if they don't cross they must be parallel

8. Two lines parallel to a third line are parallel.
True, (a lot of my answers are true >.<) in my head it seems like they would have to be... i hope these explanations aren't too vague lol

9. Two lines perpendicular to a third line are parallel.
TRUE! they would be shooting off at the same direction...

10. Two planes parallel to a line are parallel.
idk... i want to say true again but i doubt all these are true

11. Two lines parallel to a plane are parallel.
False, I picture in my head a plane and then a line parallel to it on the xy axis and one on the zy axis

The Attempt at a Solution

 

[Mark44]

Homework Statement

I only get one chance at getting these ALL right... Nazi teacher :P lol

1. Two planes parallel to a third plane are parallel.
True, planes take up a lot of space so this seems reasonable :P

Instead of a reason such as "planes take up a lot of space" think about the normals to the planes.

2. Two lines either intersect or are parallel.
False, there is a lot of space for both of them i think

Presumably you're working in three-dimensional space. In the plane, lines either intersect or are parallel. In space, can you come up with an example of lines that don't intersect and aren't parallel?

3. Two planes perpendicular to a third plane are parallel.
True Normal vectors perpendicular to a plane are parallel so I suspect this to be true

Again, think about normals to the planes.

4. Two planes perpendicular to a line are parallel.
True, in my head I'm picturing a line on the xy axis. all the planes coming off of it are parallel.

There is no "xy" axis. Are you talking about the x-axis, y-axis, or x-y plane?

5. A plane and a line either intersect or are parallel.
False, I'm imaging a line that is bound to the xy axis and a plane going past it without touching it.

A line in the x-y plane? How does the plane "go past" it? Can you describe what you're thinking more precisely?

6. Two lines perpendicular to a plane are parallel
True, picturing this in my head I believe they would have to be

Think about direction vectors for the lines and a normal for the plane.

7. Two planes either intersect or are parallel.
True, Planes are big and if they don't cross they must be parallel

Planes are "big"? In what sense? Your reason isn't very good.

8. Two lines parallel to a third line are parallel.
True, (a lot of my answers are true >.<) in my head it seems like they would have to be... i hope these explanations aren't too vague lol

This and several others are very vague. T/F questions are pretty silly, IMO, as you can flip a coin and have a reasonable chance of getting the right answer. If you are graded on your reasoning, though, many of your reasons here would not get credit.

9. Two lines perpendicular to a third line are parallel.
TRUE! they would be shooting off at the same direction...

No, this is false.

10. Two planes parallel to a line are parallel.
idk... i want to say true again but i doubt all these are true

This is false. For example, the vector <0, 0, 1> is parallel to both the x-z plane and the y-z plane, but these two planes aren't parallel to each other.

11. Two lines parallel to a plane are parallel.
False, I picture in my head a plane and then a line parallel to it on the xy axis and one on the zy axis

Again, there is no x-y axis nor is there a y-z axis. These are planes.

The Attempt at a Solution