i) In three dimensions, show that f(x, y, z) = 1/r satisfies Laplace's equation.Show this first in Cartesian coordinates and then in spherical polar coordinates.ii) If a point has spherical coordinates (4,0, 7), what are its Cartesian coordi-nates? Draw a picture.iii) A fellow student claims that the curl in spherical polar coordinates has theform1V x A=(sin 0A,) – (40) £r sin 0 \a01(A,)sin 0 dø(rA6))0+(r Ae)(rA,)) .-OrUse dimensional arguments to find their error.

(i) The Laplace equation for a function u in cartesian coordinates is defined as :…

Answered: i) In three dimensions, show that f(x,…

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i) In three dimensions, show that f(x, y, z) = 1/r satisfies Laplace's equation. Show this first in Cartesian coordinates and then in spherical polar coordinates.