If x = r sinθ cos ϕ, y = r sinθ sin ϕ and z = r cos θ, then

1.	If x = r sinθ cos ϕ, y = r sinθ sin ϕ and z = r cos θ, then .....(A) x2 + y2 + z2 = r2(B) x2 + y2 - z2 = r2(C) x2 - y2 + z2 = r2(D) x2 + y2 - z2 = r2
Answer» The correct option is: (A) x² + y²+ z² = r² Explanation: x = r sinθ cos ϕ ...(i) y = r sinθ sin ϕ ....(ii) z = r cos θ ....(iii) Squaring and adding (i) and (ii), we get x² + y² = r² sin²θ ....(iv) Squaring (iii) and adding it with (iv), we get x² + y²+ z² = r²

If x = r sinθ cos ϕ, y = r sinθ sin ϕ and z = r cos θ, then .....(A) x2 + y2 + z2 = r2(B) x2 + y2 - z2 = r2(C) x2 - y2 + z2 = r2(D) x2 + y2 - z2 = r2

Answer»

The correct option is: (A) x² + y²+ z² = r²

Explanation:

x = r sinθ cos ϕ ...(i)

y = r sinθ sin ϕ ....(ii)

z = r cos θ ....(iii)

Squaring and adding (i) and (ii), we get

x² + y² = r² sin²θ ....(iv)

Squaring (iii) and adding it with (iv), we get

x² + y²+ z² = r²