Suppose that points x and y are given in Euclidean space. Point x is displaced to point x1 by(adsbygoogle = window.adsbygoogle || []).push({});

x1=x+a(x-y)

Given that a is positive number, how can it be shown that the distance x1 to y is larger than distance x to y. I'm mainly interested in a vector interpretation of the above update rule. In that sense, can (x-y) in the above rule be interpreted as

direction (force) from point y to point x? Similar interpretation is welcome.

Given negative a, the update is x1=x+a(y-x), so now the above intuition of a force is direction from point x to point y.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Understanding displacements of points by interpreting directions

**Physics Forums | Science Articles, Homework Help, Discussion**