Final answer:
The flux of a vector field through a surface is calculated using the dot product of the field and the surface normal, integrated over the surface area.
Step-by-step explanation:
The question is asking about the flux of a vector field across a given surface. Flux is a concept from Electromagnetism in Physics, specifically dealing with how much of a field 'passes through' a given surface. Given a constant vector field f(x,y,z) = 8i - 9k, the flux Φ through a surface S can be calculated using the integral of the vector field dot product with the surface normal În over the area of the surface: Φ = ∫S f · În da. The provided examples suggest dealing with electric fields and magnetic fields, which are common contexts where flux is calculated.