91. Distances between points in a plane do not change when a coordinate system is rotated. In other words, the magnitude of a vector is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle o to become a new yxp- xo)² + (Yp- y@² = Vcx°p – x'q}² + (v'p- y' q}². coordinate system S' , as shown in the following figure. A point in a plane has coordinates (x, y) in S and coordinates (*, у) in S'. S (a) Show that, during the transformation of rotation, the coordinates in S' are expressed in terms of the coordinates in S by the following relations: S' Sx =x cos o + y sin o ly = -x sin o + ycos q' (b) Show that the distance of point P to the origin is invariant under rotations of the coordinate system. Here, you have to show that ? + y² = \&°² + y?. (c) Show that the distance between points P and Q is invariant under rotations of the coordinate system. Here, you have to show that

91. Distances between points in a plane do not change when a coordinate system is rotated. In other words, the magnitude of a vector is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle o to become a new yxp- xo)² + (Yp- y@² = Vcx°p – x'q}² + (v'p- y' q}². coordinate system S' , as shown in the following figure. A point in a plane has coordinates (x, y) in S and coordinates (*, у) in S'. S (a) Show that, during the transformation of rotation, the coordinates in S' are expressed in terms of the coordinates in S by the following relations: S' Sx =x cos o + y sin o ly = -x sin o + ycos q' (b) Show that the distance of point P to the origin is invariant under rotations of the coordinate system. Here, you have to show that ? + y² = \&°² + y?. (c) Show that the distance between points P and Q is invariant under rotations of the coordinate system. Here, you have to show that

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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Question

91. Distances between points in a plane do not change
when a coordinate system is rotated. In other words, the
magnitude of a vector is invariant under rotations of the
coordinate system. Suppose a coordinate system S is
rotated about its origin by angle o to become a new
yxp- xo)² + (Yp- y@² = Vcx°p – x'q}² + (v'p- y' q}².
coordinate system S' , as shown in the following figure. A
point in a plane has coordinates (x, y) in S and coordinates
(*, у) in S'.
S
(a) Show that, during the transformation of rotation, the
coordinates in S' are expressed in terms of the coordinates
in S by the following relations:
S'
Sx =x cos o + y sin o
ly = -x sin o + ycos q'
(b) Show that the distance of point P to the origin is
invariant under rotations of the coordinate system. Here,
you have to show that
? + y² = \&°² + y?.
(c) Show that the distance between points P and Q is
invariant under rotations of the coordinate system. Here,
you have to show that

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