Suppose γ:R→R^3 is a curve such that γ^' (t)=A_γ (t) and A are a Skew-symmetric matrix. Show γ is located on a circle. If a and b are two units vector perpendicular to each other on a plane containing a circle, parametrization with γ in terms of length, and explicitly write its representation in the coordinate system (a, b).Note: The matrix A is called Skew-symmetric matrix, if we have j,i for each: A(i,j)=-A(j,i) Suppose y: R → R³ is a curve such that y'(t) = A,(t) andA are a Skew-symmetric matrix. Show y is located on a%3|circle. If a and b are two units vector perpendicular to eachother on a plane containing a circle, parametrization within terms of length, and explicitly write its representation inthe coordinate system (a, b).Note: The matrix A is called Skew-symmetric matrix, if wehave j, i for each: A(i, j) = -A(j,i)

γ:R→R3γt=t+t2,-t,-t2 If i represent this in the form of matrix it will be represented in following…

Answered: Suppose γ:R→R^3 is a curve such that…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose γ:R→R^3 is a curve such that γ^' (t)=A_γ (t) and A are a Skew-symmetric matrix. Show γ is located on a circle. If a and b are two units vector perpendicular to each other on a plane containing a circle, parametrization with γ in terms of length, and explicitly write its representation in the coordinate system (a, b).
Note: The matrix A is called Skew-symmetric matrix, if we have j,i for each: A(i,j)=-A(j,i)

Suppose y: R → R³ is a curve such that y'(t) = A,(t) and
A are a Skew-symmetric matrix. Show y is located on a
%3|
circle. If a and b are two units vector perpendicular to each
other on a plane containing a circle, parametrization with
in terms of length, and explicitly write its representation in
the coordinate system (a, b).
Note: The matrix A is called Skew-symmetric matrix, if we
have j, i for each: A(i, j) = -A(j,i)

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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