Question

How to solve given attachement Q-7

Answer 1

x=rsinθ.cosΦ

y=rsinθ.sinΦ

z=rcosθ

SQUARING AND ADDING THE EQUATIONS

x² + y² + z²= r²sin²θ.cos²Φ + r²sin²θ.sin²Φ + r²cos²θ

x² + y² + z²= r²(sin²θ.cos²Φ + sin²θ.sin²Φ + cos²θ)

x² + y² + z²= r²(sin²θ(cos²Φ + sin²Φ )+ cos²θ)

cos²Φ + sin²Φ =1

x² + y² + z²= r²(sin²θ+ cos²θ)

sin²θ+ cos²θ=1

x² + y² + z²= r²

∴ x² + y² + z² is independent of θ,Φ