Planes in R3 Properties: Are They Parallel or Intersecting?

In summary, the conversation is about determining which statements are true in a given scenario related to lines and planes. A definition of parallel is requested and the conversation ends with the clarification that statement A is true but B is false. The person will continue working on the problem later.
  • #1
dGasim
16
0
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
 
Physics news on Phys.org
  • #2
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?
 
Last edited:
  • #3
if two lines are skew they are neither intersecting nor are parallel
 
  • #4
dGasim said:
if two lines are skew they are neither intersecting nor are parallel

I asked, what's your DEFINITION of parallel?
 
  • #5
Oh. Sorry. I'll draw it tonight. I just have to rush to a store right. Sorry about that. Thanks.
 
  • #6
dGasim said:
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.
 
  • #7
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.
 
  • #8
dGasim said:
Actually, I get it. A is true but B is false. Am I right on this?

Correct so far.
 
  • #9
Alright, I am going to be working on this tonight. Thank you for pointing that out!
 

Related to Planes in R3 Properties: Are They Parallel or Intersecting?

1. What are the properties of planes in R3?

Planes in R3, or three-dimensional space, have several important properties. They are flat surfaces that extend infinitely in all directions and are defined by three non-collinear points or a point and a normal vector. They also have a specific equation, ax + by + cz = d, where a, b, and c are the coefficients of the variables x, y, and z, and d is a constant.

2. How are planes in R3 different from planes in R2?

Planes in R3 are similar to planes in R2, but they have an additional dimension. This means that they can intersect with each other in a line, rather than just a single point. In R3, planes are also described by three variables, whereas in R2 they only have two variables.

3. Can planes in R3 be parallel to each other?

Yes, planes in R3 can be parallel to each other. This means that they never intersect and have the same slope or normal vector. In terms of their equations, parallel planes have the same values for a, b, and c, but different values for d.

4. How do you determine the intersection of two planes in R3?

The intersection of two planes in R3 can be determined by solving their equations simultaneously. If the planes are not parallel, they will intersect in a line. If they are parallel, they will either have no intersection or will be the same plane.

5. What is the relationship between a point and a plane in R3?

A point and a plane in R3 can have different relationships depending on the position of the point in relation to the plane. A point can be on the plane, above the plane, below the plane, or even on the opposite side of the plane. This relationship can be determined by plugging in the coordinates of the point into the equation of the plane.

Similar threads

Lagrange multipliers understanding
    • Calculus and Beyond Homework Help
Replies
8
Views
570
Applying Stokes' Theorem to the part of a Sphere Above a Plane
    • Calculus and Beyond Homework Help
Replies
21
Views
3K
Are These Geometry Statements True or False?
    • Calculus and Beyond Homework Help
Replies
1
Views
3K
Property of compact convex sets of width 1
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Distance between two parallel lines
    • Calculus and Beyond Homework Help
Replies
2
Views
1K
B Existence of parallels in axiomatic plane geometries
    • General Math
2
Replies
36
Views
4K
Understanding Parallel Lines: Definition and Differences
    • Calculus and Beyond Homework Help
Replies
8
Views
2K
MHB Relationship between three planes
    • Linear and Abstract Algebra
Replies
5
Views
1K
How do I find a plane that contains two given lines?
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Let A, B, and C be vectors in R3....prove r lies in a plane
    • Calculus and Beyond Homework Help
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top