Question

If v = xz - xy yz, express v in cylindrical coordinates

Answer 1

To express v = xz - xyyz in cylindrical coordinates, we substitute x = rcos(θ), y = rsin(θ), and z = z, resulting in v = rcos(θ)z - r²sin(θ)cos(θ)z.

Step-by-step explanation:

In cylindrical coordinates, a point is described by its radius (r), angle (θ), and height (z). To express v = xz - xyyz in cylindrical coordinates, we need to substitute the corresponding expressions for x, y, and z.

For x, we have x = rcos(θ).

For y, we have y = rsin(θ).

For z, we have z = z.

Substituting these expressions into v, we get v = (rcos(θ))(z) - (rcos(θ))(rsin(θ))(z).

So, in cylindrical coordinates, v is expressed as v = rcos(θ)z - r²sin(θ)cos(θ)z.