A 4-vector has components V#= (1,3, 5, 2) in the coordinate Cartesian basis at some point p in spacetime. (a) Compute Vn using the Minkowski metric. (b) How do the components of V, change under a coordinate transformation from z to z? Find V for the transformation: %3D t=t', z=r sin e cos o, y =r sin ở sin o, zr cos 6. at the point r= 5.1, 0 = 1.25, o = 0.2

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 49E
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A 4-vector has components V = (1,3, 5, 2) in the coordinate Cartesian basis at some point p in spacetime.
(a) Compute Vµ using the Minkowski metric.
(b) How do the components of Vµ change under a coordinate transformation from z" to a? Find V for
the transformation:
%3D
t =t',
z = r sin 0 cos ó,
y =r sin 6 sin ø ,
z=r cos 0,
at the point r = 5.1, 0 = 1.25, ø = 0.2
%3D
Transcribed Image Text:A 4-vector has components V = (1,3, 5, 2) in the coordinate Cartesian basis at some point p in spacetime. (a) Compute Vµ using the Minkowski metric. (b) How do the components of Vµ change under a coordinate transformation from z" to a? Find V for the transformation: %3D t =t', z = r sin 0 cos ó, y =r sin 6 sin ø , z=r cos 0, at the point r = 5.1, 0 = 1.25, ø = 0.2 %3D
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