For spherical coordinates
x = r sinθ cosφ
y = r sinθ sinφ
z = r cosθ
Hence, dx = dr sinθcosφ + dθr cosθcosφ – dφ rsinθ sinφ ...(1)
dy = dr sin θ sin φ + d θ r cos θ sin φ + d φ r sin θ cos φ ...(2)
and dz = dr cos θ – d θ r sin θ ...(3)
Squaring and adding (1), (2) and (3), we have
dx2 + dy2 + dz2 = ds2 = dr2 + r2dθ2 + r2sin2θ d φ2
Hence, h1 = 1, ⇒ h1 = 1, h2 = r, h3 = r sin θ
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