# What does colinear mean?

• Mar 19th 2011, 03:14 PM
divinelogos
What does colinear mean?
I'm trying to see if I understand the concept of colinearity. Is the following defition correct?

Two vectors are colinear if and only if they both form segments of the same ray.

Or can two vectors be colinear if they are parallel, because vectors don't really have a "position"?

Thanks for the help!
• Mar 19th 2011, 03:19 PM
dwsmith
Quote:

Originally Posted by divinelogos
I'm trying to see if I understand the concept of colinearity. Is the following defition correct?

Two vectors are colinear if and only if they both form segments of the same ray.

Or can two vectors be colinear if they are parallel, because vectors don't really have a "position"?

Thanks for the help!

Collinear if they lie along the same line or are parallel.
• Mar 19th 2011, 04:30 PM
Plato
Quote:

Originally Posted by divinelogos
I'm trying to see if I understand the concept of colinearity. Is the following defition correct?
Two vectors are colinear if and only if they both form segments of the same ray.

On one level this is a totally meaningless question.
Consider the points $A;(1,3),~B:(2,4),~C:(1,2),~\&~D:(2,3)$
If one plots those four point it is transparently clear that those four points are not collinear.
BUT $\overrightarrow {AB} = \overrightarrow {CD}$!
Under any common understanding of the language, don’t you think that a vector ought to be collinear with itself?
Do those two vectors form segments of the same ray?

NO! This is just a problematic question. The author may not fully understand the mathematical status of vectors
A vector is an equivalence class of object having the same direction and same length.

Thus two non zero vectors are collinear if and only if they are multiples of each other.
• Mar 19th 2011, 06:44 PM
divinelogos
Quote:

Originally Posted by Plato
On one level this is a totally meaningless question.
Consider the points $A;(1,3),~B:(2,4),~C:(1,2),~\&~D:(2,3)$
If one plots those four point it is transparently clear that those four points are not collinear.
BUT $\overrightarrow {AB} = \overrightarrow {CD}$!
Under any common understanding of the language, don’t you think that a vector ought to be collinear with itself?
Do those two vectors form segments of the same ray?

NO! This is just a problematic question. The author may not fully understand the mathematical status of vectors
A vector is an equivalence class of object having the same direction and same length.

Thus two non zero vectors are collinear if and only if they are multiples of each other.

"Two vectors are colinear if and only if they form segments of the same way" was to distinguish between two ways of defining the collinearity of two vectors. That is, are two vectors colinear if they "lie on the same line" (as dwsmith said), or can they be parallel as well? Your answer seems to imply, Plato, that two vectors are colinear if and only if the simultaneous "extending" of both vectors creates a line. Thus, if two vectors are parallel, they are not colinear. Is this correct?