Vectors - shortest distance

In summary, the shortest distance between the two vectors a and b can be calculated by finding the length of one line perpendicular to a and the other perpendicular to b, both meeting at the same endpoint. There is no direct distance between the two vectors themselves.
  • #1
nokia8650
219
0
Say you have two vectors: a and b.

Is the shortest distance between these two vectors when a line perpendicular to a meets vector b, or when a line perpendicular to vector b meets vector a?

Thanks
 
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  • #2
nokia8650 said:
Say you have two vectors: a and b.

Is the shortest distance between these two vectors when a line perpendicular to a meets vector b, or when a line perpendicular to vector b meets vector a?

Thanks

Hi nokia8650! :smile:

The length of one line is a.cosθ, and of the other is b.cosθ.

But those are the distances between one line and the other endpoint.

There is no such thing as the distance between two vectors … only between their endpoints.
 

1. What is the shortest distance between two vectors?

The shortest distance between two vectors is the length of the shortest path connecting the two vectors. This path is also known as the shortest vector.

2. How do you calculate the shortest distance between two vectors?

To calculate the shortest distance between two vectors, you can use the formula: d = |v1 - v2|, where d is the shortest distance, v1 and v2 are the two vectors, and | | represents the magnitude or length of the vector.

3. Can the shortest distance between two vectors be negative?

No, the shortest distance between two vectors cannot be negative. It represents the length of a path, which is always a positive value.

4. What is the significance of the shortest distance between two vectors?

The shortest distance between two vectors is important in many applications, such as physics, engineering, and computer graphics. It helps determine the minimum distance between two objects or points and is useful in solving optimization problems.

5. Are there any real-life examples where the concept of shortest distance between vectors is used?

Yes, there are many real-life examples where the concept of shortest distance between vectors is used. For instance, in navigation systems, the shortest distance between two locations is used to calculate the shortest route. In physics, it is used to find the minimum distance between two moving objects. In computer graphics, it is used to determine the distance between a point and a line or a point and a surface.

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