Finding distance between vectors

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In summary, to determine the distance from $\vec{A}$ to $\vec{B}$, you can convert the given cylindrical coordinates to Cartesian coordinates and use the standard formula for distance.
  • #1
Drain Brain
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Given $\vec{A}=2.15a\rho+6.25a\phi+3az$ and $\vec{B}=0.11a\rho+3.35a\phi+2az$. Determine the distance from $\vec{A}$ to $\vec{B}$.


what to do first?
 
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  • #2
This question doesn't make a whole lot of sense. I am assuming you are dealing with a cylindrical polar orthonormal system, which is fine. But there is no such thing as finding "distances between vectors", because vectors do NOT have any position! All they have is direction and magnitude. That is why they can be picked up and moved anywhere you like.
 
  • #3
maybe the problem is asking about a vector from A to B.
How can I do that?
 
  • #4
You can convert cylindrical coordinates to Cartesian coordinates and use the standard formula for distance.
 

FAQ: Finding distance between vectors

What is the definition of distance between vectors?

The distance between two vectors is the length of the shortest path between their two endpoints. It is a measure of the magnitude of the difference between the two vectors.

How do you calculate the distance between two vectors?

The distance between two vectors can be calculated using the Pythagorean theorem. First, find the difference between each corresponding component of the two vectors. Then, square each difference, add them together, and take the square root of the sum to find the distance.

Can the distance between two vectors be negative?

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

What is the significance of finding the distance between vectors in scientific research?

Finding the distance between vectors is important in many fields of science, such as physics, engineering, and biology. It can be used to measure the magnitude of a change or difference in a system, and can also help determine relationships between different variables.

Are there different methods for finding the distance between vectors?

Yes, there are multiple methods for finding the distance between vectors, such as using the Pythagorean theorem, trigonometric functions, or vector operations. The method used may depend on the specific application or context in which the distance is being calculated.

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