Mark the correct alternative in the following:
If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x2 + y2 + z2 is independent of
Given:
X = r sin θ cos ϕ
Y = r sin θ sin ϕ
Z = r cos θ
⇒ x2+y2+z2
⇒ (r sin θ cos ϕ )2 + (r sin θ sin ϕ) 2 + (r cos θ )2
⇒ r2sin2θcos2ϕ + r2sin2θsin2ϕ + r2cos2θ
⇒ r2sin2θ(cos2ϕ+ sin2ϕ) + r2cos2θ
⇒ r2sin2θ + r2cos2θ
⇒ r2(sin2θ + cos2θ)
⇒ r2.
∴ It is independent of θ and ϕ .