Express the unit vectors r, , in terms of x, y, z (that is, derive Eq.

Express the unit vectors r, θ, Ф in terms of x, y, z (that is, derive Eq. 1.64). Check your answers several ways (r ∙ r = 1, θ ∙ Ф = r x θ = Ф , .... ). Also work out the inverse formulas, giving x, y, z in terms of r, θ ∙ Ф (and θ, Ф).