Final answer:
To express v in cylindrical coordinates, the given expression v = xz - xy + yz can be converted into cylindrical coordinates as v = (ρz, -ρsinθcosθ, zρsinθ).
Step-by-step explanation:
To express v in cylindrical coordinates, we need to convert the given expression into cylindrical coordinates. In cylindrical coordinates, the displacement vector v can be expressed as:
v = (vρ, vθ, vz)
where ρ is the distance from the z-axis, θ is the angle from the positive x-axis to the projection of the point on the xy-plane, and z is the height of the point above the xy-plane.
For the given expression v = xz - xy + yz, we can express it in cylindrical coordinates as v = ρz - ρsinθcosθ + zρsinθ. Therefore, v can be expressed as v = (ρz, -ρsinθcosθ, zρsinθ) in cylindrical coordinates.