Determine the value of ∬SF⃗⋅dS⃗\iint_S \vec{F} \cdot d\vec{S}∬SF⋅dS for F⃗=⟨x3,y3,z3⟩\vec{F} = \langle x^3, y^3, z^3 \rangleF=⟨x3,y3,z3⟩ and SSS the unit sphere x2+y2+z2=1x^2+y^2+z^2=1x2+y2+z2=1.
45π\frac{4}{5}\pi54π
125π\frac{12}{5}\pi512π
π\piπ
35π\frac{3}{5}\pi53π