Planes in R3 Properties: Are They Parallel or Intersecting?

[dGasim]

Hello I am having a problem with the following question.

Homework Statement

Determine which statements are true in 3. (Select all that apply.)

(a) Two lines parallel to a third line are parallel.
(b) Two lines perpendicular to a third line are parallel.
(c) Two planes parallel to a third plane are parallel.
(d) Two planes perpendicular to a third plane are parallel.
(e) Two lines parallel to a plane are parallel.
(f) Two lines perpendicular to a plane are parallel.
(g) Two planes parallel to a line are parallel.
(h) Two planes perpendicular to a line are parallel.
(i) Two planes either intersect or are parallel.
(j) Two lines either intersect or are parallel.
(k) A plane and a line either intersect or are parallel.

Homework Equations

None.

The Attempt at a Solution

This is what I did (i am going to write it with T/F)
a) F - they maybe skew
b) T
c) T
d) T
e) F - they maybe skew
f) T
g) F - they may intersect
h) T
i) T
j) F - Skew
k) T? - I choose true but a line can be contained in a plane. Are they different things? Or I have a problem in other answers.

Thanks in advance,
Gasim

 

[Dick]

If by '3' you mean three dimensional euclidean space, then a) is already wrong. What's your definition of parallel? Can you give an example where the two lines are skew?

 

[dGasim]

if two lines are skew they are neither intersecting nor are parallel

 

[Dick]

if two lines are skew they are neither intersecting nor are parallel

I asked, what's your DEFINITION of parallel?

 

[dGasim]

Oh. Sorry. I'll draw it tonight. I just have to rush to a store right. Sorry about that. Thanks.

 

[Dick]

Oh. Sorry. I'll draw it tonight. I just have to rush to a store right. Sorry about that. Thanks.

S'ok, but you'll probably have to do more than draw it. That wouldn't likely be useful. State the definition in words.

 

[dGasim]

Actually, I get it. A is true but B is false. Am I right on this?

Skew is like one of them for example is a straight line to the right and the other one in the bottom of it towards me. Its not a good example but I hope its right.

 

[Dick]

Actually, I get it. A is true but B is false. Am I right on this?

Correct so far.

 

[dGasim]

Alright, I am going to be working on this tonight. Thank you for pointing that out!