Distance formula in 3 dimensions

Click For Summary
SUMMARY

The discussion focuses on calculating the shortest distance in three-dimensional space using the Pythagorean theorem. The solution involves determining the hypotenuse (X) of a triangle formed by the height (Z) and length (Y), where X represents the distance from a point on the x-axis to a given point (a, b, c). The key takeaway is that the shortest distance is always a straight line, and visualizing the problem with a triangle aids in understanding the relationship between the coordinates.

PREREQUISITES
  • Understanding of the Pythagorean theorem
  • Familiarity with three-dimensional coordinate systems
  • Basic knowledge of geometry and triangles
  • Ability to visualize geometric relationships
NEXT STEPS
  • Research the application of the Pythagorean theorem in three dimensions
  • Explore geometric visualization techniques for complex problems
  • Learn about distance minimization in calculus
  • Investigate the use of coordinate transformations in geometry
USEFUL FOR

Students, mathematicians, and anyone interested in geometry, particularly those working with three-dimensional space and distance calculations.

Rock32
Messages
12
Reaction score
0
Edit*: problem solved. Thanks for the hint Dick.
 
Last edited:
Physics news on Phys.org
Try the pythagorian theorem: x = sqrt(y^2 + z^2)

Since you can have any value on the x axis, the shortest distance will always be a straight line.

To see it better, draw out a triangle, where Z is the height, and Y is the lenght, leaving the distance X which will be the hypotenuse.

Draw it out, it'll make it clear.

EDIT: X,Y,Z in your case being points A,B,C
 
A point on the x-axis is given by (d,0,0) for some value of d. What value of d will minimize the distance to (a,b,c)?
 

Similar threads

Given specific v, dimension of subspace of L(V, W) where Tv=0?
  • · Replies 15 ·
Replies
15
Views
2K
What is meant by compex dimension? (Abstract algebra)
  • · Replies 5 ·
Replies
5
Views
1K
Finding the dimension of a subspace
  • · Replies 7 ·
Replies
7
Views
2K
What Are the Dimensions of the Least Expensive Conical Frustum Container?
  • · Replies 12 ·
Replies
12
Views
2K
Find the dimensions that will minimize the surface area of a Rectangle
  • · Replies 1 ·
Replies
1
Views
2K
Modular Forms, Dimension, Valence Formula
  • · Replies 5 ·
Replies
5
Views
2K
Vector space of functions defined by a condition
  • · Replies 58 ·
2
Replies
58
Views
5K
Solving a partial differential equation
  • · Replies 3 ·
Replies
3
Views
1K
Dimension of orthogonal subspaces sum
  • · Replies 4 ·
Replies
4
Views
2K
Insights Aspects Behind the Concept of Dimension in Various Fields
  • · Replies 2 ·
Replies
2
Views
6K