# 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 ofA. θ, ϕB. r, θC. r, ϕD. r

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 .

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