Coordinate Distance Calculation

[bignum]

Homework Statement

When you have a point in $$\Re$$³, like for example let J(3, 7, 3) and Q(1, 2, 3). What is the distance in terms of coordinate between them? Like can you just subtract the corresponding components?

Homework Equations

I am not sure if it only works for the formula distance formula.

The Attempt at a Solution

Like what I meant was if I should try subtracting from J to Q to find (...)

J - Q = (2, 5, 0)

Does that work?

Thank you

 

[eok20]

J-Q is the vector from Q to J. The distance between Q and J is the magnitude of J-Q, which is sqrt(2^2 + 5^2 + 0^2)

 

[bignum]

J-Q is the vector from Q to J. The distance between Q and J is the magnitude of J-Q, which is sqrt(2^2 + 5^2 + 0^2)

I know how to use the distance formula, but I am wondering if I can just subtract the corresponding components. Because I am reading Mathematical Methods in Physical Science by Wiley and they subtracted the components like so

 

[Tedjn]

Yes, in order to get the displacement vector, you can just subtract components element by element. This makes sense if you think about J and Q as vectors from the origin and the displacement vector going from the head of J to the tail of Q. To find the distance, as mentioned above, you need to get the length of that vector. This procedure turns out to be equivalent to the distance formula.

 

[bignum]

Yes, in order to get the displacement vector, you can just subtract components element by element. This makes sense if you think about J and Q as vectors from the origin and the displacement vector going from the head of J to the tail of Q. To find the distance, as mentioned above, you need to get the length of that vector. This procedure turns out to be equivalent to the distance formula.

Thank you! I was really having qualms about this.