In a fuel cell technology, membrane layer is located in between parallel catalyst layers

$($anode and cathode$)$ that permits only necessary lons to pass through between the

anode and cathode as illustraled in Figure Q$3.$ The Cartesian coordinates and direction

vector of both anode and cathode are given as follows:

Anod mempunyal ketebalan $0\mathrm{.}62$ unit dengan garis tengah yang melalui titik

$(1,5,3)$ dan satah tersebut adalah normal kepada vektor $n_1=2i-2j+1k.$

Katod mempunyai ketebalan $0\mathrm{.}45$ unit dengan garis tengah yang melalui titik

$(0,5,-2)$ dan satah tersebut adalah normal kepada vektor $n_2=6i-6j+3k.$

Anode has a thickness of $0\mathrm{.}62$ unit and its center passes through point $(1,5,3)$ and the

plane is normal to vector $n_1=2i-2j+1k.$ Cathode has a thickness of $0\mathrm{.}45$ unit and

its center passes through point $(0,5,-2)$ and normal to vector $n_2=6i-6j+3k_2.$

$($i$)$ Tentuk$$n persam$$an satah Carte$$ian untuk anod dan katod.

Determine the Cartesian equation of plane for anode and cathode.

$(2$ markah$/$ marks$)$

$($ii$)$ Tentukan ketebalan lapisan membran.

Determine the thickness of membrane layer.

$(6$ markah$/$ marks$)$

$($b$)$ Terangkan ciri kecapahan untuk aliran gas, $F(x,y,z)=($:$e^x,yz,-y{z}^2$:$)$ pada titik$-$

titik $(0,2,-1),(1,3,2)$ dan $(0,1,1)$ masing$-$masing. Terangkan ciri ikal pada

titik yang mempunyai gas tidak boleh dimampat sahaja daripada $3$ titik ini.

Seterusnya, lakarkan arah putaran untuk aliran gas pada titik yang dipilih ini.

Explain the divergence characteristic of the gas flow of $F(x,y,z)=(e^x,y{z}_4-y{z}^2)$ at

points $(0,2,-1),(1,3,2)$ and $(0,1,1)$ respectively. Explain the cur characteristic at the

point that has incompressible gas flow only from these $3$ points. Hence, sketch the

rotational direction of the gas flow at this selected point.