Are parallel vectors always in the same direction?

In summary, the conversation revolves around the definition of parallel vectors and how it differs in mathematics and physics. It is agreed that in mathematics, two lines must have an angle of 0 or 180 degrees to be considered parallel, while in physics, vectors can have an angle of 0 or 180 degrees and still be considered parallel or anti-parallel. The difference in terminology is discussed, with the conclusion that it is acceptable to use the terms "parallel" or "anti-parallel" depending on the context.
  • #1
venomnert
6
0
I am just starting to learn about vectors and I have question regarding vectors and their parallel properties:

Assume that we have two vectors A and B, and they are said to be parallel. We know that in order to be parallel the angle between the two vectors either have to be 0 or 180. However, after consulting StackOverFlow, I am told that "Two vectors are parallel if they have the same direction". Thus, eliminating the fact that the angle between the vectors can't be 180.

So my question is, can someone verify the statement, if two vectors are in the same direction then they are parallel and have an angle of 0.
 
Physics news on Phys.org
  • #2
venomnert said:
So my question is, can someone verify the statement, if two vectors are in the same direction then they are parallel and have an angle of 0.
That statement is certainly true. But I believe the most useful definition of "parallel vectors" would allow them to have an angle of 0 or 180. (Some call vectors with an angle of 0 parallel and those with an angle of 180 anti-parallel.)

What's the physics context of your question?
 
  • Like
Likes venomnert
  • #3
Doc Al said:
That statement is certainly true. But I believe the most useful definition of "parallel vectors" would allow them to have an angle of 0 or 180. (Some call vectors with an angle of 0 parallel and those with an angle of 180 anti-parallel.)

What's the physics context of your question?
Okay, so for the statement "A unit vector is labeled by a caret; the vector of unit length parallel to A is A(caret)". The unit vector of A is in the same direction as A since it 's parallel. Had they said it was anti-parallel, the angle would be 180 and the vectors would be opposite in direction.
 
  • #4
The unit vector and vector A are collinear.
 
Last edited by a moderator:
  • Like
Likes venomnert
  • #5
venomnert said:
We know that in order to be parallel the angle between the two vectors either have to be 0 or 180.
I don't think that this statement is correct. When angle between two lines ( not vectors) is either 0 or 180 then they are collinear. When we come to vector then we need to understand that vectors are not mere straight lines . They have a direction too. So if angle between two vectors is 180 they are not parallel but oppositely directed and hence called anti-parallel. One need to understand that there is a difference between Maths and Physics. Take the example of two men one traveling towards North and other towards South. If you say that their paths are parallel then how do you distinguish between them?
 
  • #6
Take the example of two men one traveling towards North and other towards South. If you say that their paths are parallel then how do you distinguish between them?

In term of Physics, since they are both traveling the opposite direction they are anti-parallel.
 
  • #7
venomnert said:
Take the example of two men one traveling towards North and other towards South. If you say that their paths are parallel then how do you distinguish between them?
Well, they have different directions!

venomnert said:
In term of Physics, since they are both traveling the opposite direction they are anti-parallel.
That's fine.

But it is perfectly reasonable to call those two men as traveling in parallel paths. (I would not get too hung up on this terminology.)
 
  • #8
Well, they would be traveling along parallel lines, but the vectors are not parallel.
 
  • #9
Khashishi said:
Well, they would be traveling along parallel lines, but the vectors are not parallel.
Why not? What definition of "parallel" are you using?
 
  • #10
Doc Al said:
Why not? What definition of "parallel" are you using?

My take is that when you use the word parallel in context of Maths then two lines having an angle between them as 180 can be called parallel more correctly co-linear. In Physics the nuances of the same word is lightly different and in such a case we call two vectors as anti-parallel. Don't know whether it is acceptable to you.
 

1. What is a vector?

A vector is a mathematical object that has both magnitude (or length) and direction. It is often represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude.

2. What does it mean for two vectors to be parallel?

Two vectors are parallel if they have the same direction or are in the opposite direction, regardless of their magnitude. This means that they will never intersect or cross each other.

3. How do you determine if two vectors are parallel?

To determine if two vectors are parallel, you can use the dot product. If the dot product of two vectors is equal to the product of their magnitudes, then the vectors are parallel. Alternatively, you can also compare the direction ratios of the two vectors. If the direction ratios are equal, then the vectors are parallel.

4. What is the difference between a vector and a scalar?

While a vector has both magnitude and direction, a scalar only has magnitude. This means that a scalar is just a single number, whereas a vector has multiple components (such as x, y, and z) that represent different directions and magnitudes.

5. How do you find the direction of a vector?

To find the direction of a vector, you can use the direction cosines or direction angles. The direction cosines are the ratio of the vector's components to its magnitude, while the direction angles are the angles the vector makes with the x, y, and z axes. You can also determine the direction of a vector by finding the unit vector in the same direction, which is a vector with the same direction but a magnitude of 1.

Similar threads

I Understanding Ewald's sphere in the context of X-Ray diffraction
    • Other Physics Topics
Replies
3
Views
3K
I A question about geodesics and notion of parallelism
    • Special and General Relativity
Replies
19
Views
1K
B A Question Relating Sum of Angles and Breaking of the Parallel Postulate
    • General Math
Replies
6
Views
509
I Non orthogonal basis and the lines of its coordinate grid
    • Linear and Abstract Algebra
Replies
9
Views
213
I Parallel Transport Along Geodesic
    • Differential Geometry
Replies
6
Views
2K
I Coriolis acceleration of a projectile launched at the equator
    • Mechanics
Replies
4
Views
870
I Parallel transport vs Lie dragging along a Killing vector field
    • Special and General Relativity
Replies
20
Views
2K
I Parallel Transport & Geodesics: Explained
    • Special and General Relativity
Replies
9
Views
2K
Vector dot product and parallel vectors
    • Precalculus Mathematics Homework Help
Replies
6
Views
3K
I What can we scientifically measure directly?
    • Other Physics Topics
Replies
27
Views
2K

Hot Threads

Recent Insights

Back
Top