Register to reply

Coplanar vectors

by 1MileCrash
Tags: coplanar, vectors
Share this thread:
1MileCrash
#1
Aug28-12, 01:24 PM
1MileCrash's Avatar
P: 1,302
Two free vectors are always coplanar.

Then if A and B are free vectors, are A, B, and A+B all coplanar in all cases?
Phys.Org News Partner Mathematics news on Phys.org
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Team announces construction of a formal computer-verified proof of the Kepler conjecture
Mark44
#2
Aug28-12, 01:53 PM
Mentor
P: 21,305
Quote Quote by 1MileCrash View Post
Two free vectors are always coplanar.

Then if A and B are free vectors, are A, B, and A+B all coplanar in all cases?
Yes.
Any two vectors that start from the same point (you can assume that they start from the origin) determine a plane. Any linear combination of these vectors (including 1*A + 1*B) also lies in that same plane.
1MileCrash
#3
Aug28-12, 02:11 PM
1MileCrash's Avatar
P: 1,302
Cool.

How about this:

If two vectors are linearly dependent, they are collinear. They are always coplanar.

If three vectors are linearly dependent, they are coplanar. Three vectors are always all co"cubeular" (I don't know a word like coplanar for a three dimensional object.)

Based on this pattern, it correct to say that:

If n vectors are linearly dependent, then they are co(n-1 space object) and are always co(n space object).

Since for two vectors, an n-1 space object is a line, for three it is a plane, and so on.

Am I making sense?

Mark44
#4
Aug28-12, 04:10 PM
Mentor
P: 21,305
Coplanar vectors

Quote Quote by 1MileCrash View Post
Cool.

How about this:

If two vectors are linearly dependent, they are collinear. They are always coplanar.
Yes. If two vectors are linearly dependent, then each is a nonzero scalar multiple of the other.
Quote Quote by 1MileCrash View Post

If three vectors are linearly dependent, they are coplanar.
They could be collinear, depending on which vectors we're talking about.
Quote Quote by 1MileCrash View Post
Three vectors are always all co"cubeular" (I don't know a word like coplanar for a three dimensional object.)
I don't believe there is any special terminalogy beyond coplanar.
Quote Quote by 1MileCrash View Post

Based on this pattern, it correct to say that:

If n vectors are linearly dependent, then they are co(n-1 space object) and are always co(n space object).

Since for two vectors, an n-1 space object is a line, for three it is a plane, and so on.

Am I making sense?
Yes, I get what you're saying, but as I said, I don't believe there is any terminology beyond coplanar.


Register to reply

Related Discussions
Proving 3 vectors are coplanar Precalculus Mathematics Homework 26
Coplanar vectors Calculus & Beyond Homework 4
Coplanar vectors Introductory Physics Homework 7
3D | coplanar vectors General Math 4