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a) Given two points with coordinates A = (XA, YA) and B = (XB,YB) in R² in a certain Cartesian system, we define the Euclidean distance between them as (Ar)² = (Ax)² + (Ay)², where Ax = xB - Xд and Aу = уB - YA. Show that the Euclidean distance is invariant to rotations, that is, (Ar)² = (Ar')² where the relationship between both coordinate system is With a constant angle. x'x cos y sin = y' x sin 0 + y cos 0

a) Given two points with coordinates A = (XA, YA) and B = (XB,YB) in R² in a certain Cartesian system, we define the Euclidean distance between them as (Ar)² = (Ax)² + (Ay)², where Ax = xB - Xд and Aу = уB - YA. Show that the Euclidean distance is invariant to rotations, that is, (Ar)² = (Ar')² where the relationship between both coordinate system is With a constant angle. x'x cos y sin = y' x sin 0 + y cos 0

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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a) Given two points with coordinates A = (XA, YA) and B = (XB,YB) in R² in a certain Cartesian system, we define the Euclidean distance between them as (Ar)² = (Ax)² + (Ay)², where Ax = xB - Xд and Aу = уB - YA. Show that the Euclidean distance is invariant to rotations, that is, (Ar)² = (Ar')² where the relationship between both coordinate system is With a constant angle. x'x cos y sin = y' x sin 0 + y cos 0
Transcribed Image Text:a) Given two points with coordinates A = (XA, YA) and B = (XB,YB) in R² in a certain Cartesian system, we define the Euclidean distance between them as (Ar)² = (Ax)² + (Ay)², where Ax = xB - Xд and Aу = уB - YA. Show that the Euclidean distance is invariant to rotations, that is, (Ar)² = (Ar')² where the relationship between both coordinate system is With a constant angle. x'x cos y sin = y' x sin 0 + y cos 0
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