Assignment:
A particle moves along a parametrized curve given by
x(λ) =cos(λ), y(λ)=sin(λ), z(λ)=λ
Express the path of the curve in the spherical polar coordinates {r, theta, pheta}
where x = rsin(θ)cos(θ)
y=rsin(θ)sin(θ)
z=rcos(θ)
so that the metric is
ds^2=dr^2+(r^2)d(θ)^2+(r^2)sin^2(θ)d(θ)^2
Calculate the components of the tangent vector to the curve in both Cartesian and spherical polar coordinate systems.
Provide complete and step by step solution for the question and show calculations and use formulas.