(a) Express the spherical unit vectors ê, ê, in terms of the Cartesian unit vectors✰, ŷ, 2 (that is, derive Eq. 1.64 of Griffiths). Also work out the inverse formulas,giving ✰, ŷ, 2 in terms of f, 0, $ (and 0, $). Calculate af/00 and af/ap, andexpress them in terms of spherical unit vectors.(b) Express the cylindrical unit vectors ŝ, , 2 in terms of the Cartesian unit vec-tors î, ŷ, 2 (that is, derive Eq. 1.75 of Griffiths). Also work out the inverseformulas, giving x, ŷ, 2 in terms of ŝ, $, 2 (and ). Show that af/0 = $.

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(a) Express the spherical unit vectors f, 0, $ in terms of the Cartesian unit vectors Î, ŷ, 2 (that is, derive Eq. 1.64 of Griffiths). Also work out the inverse formulas, giving ✰, ŷ, 2 in terms of f, ô, § (and 0, 4). Calculate af/00 and Əf/3, and express them in terms of spherical unit vectors. (b) Express the cylindrical unit vectors ŝ, $, 2 in terms of the Cartesian unit vec- tors Â, ŷ, 2 (that is, derive Eq. 1.75 of Griffiths). Also work out the inverse formulas, giving Â, ŷ, 2 in terms of ŝ, §, 2 (and ø). Show that dî/0¢ = §.

(a) Express the spherical unit vectors f, 0, $ in terms of the Cartesian unit vectors Î, ŷ, 2 (that is, derive Eq. 1.64 of Griffiths). Also work out the inverse formulas, giving ✰, ŷ, 2 in terms of f, ô, § (and 0, 4). Calculate af/00 and Əf/3, and express them in terms of spherical unit vectors. (b) Express the cylindrical unit vectors ŝ, $, 2 in terms of the Cartesian unit vec- tors Â, ŷ, 2 (that is, derive Eq. 1.75 of Griffiths). Also work out the inverse formulas, giving Â, ŷ, 2 in terms of ŝ, §, 2 (and ø). Show that dî/0¢ = §.