Let TT be the triangular region with vertices $(1,0,0)(1,0,0),(0,1,0)(0,1,0),$ and $(0,0,1)(0,0,1)$ oriented with upward$-$pointing normal vector.

A fluid flows with constant velocity field v$=8$i$+3$j$$m$/$sv$=8$i$+3$j$$m$/$s$.$ Calculate:

$($a$)$ The flow rate through TT

$($b$)$ The flow rate through the projection of TT onto the xyxy$-$plane $[$the triangle with vertices $(0,0,0)(0,0,0),(1,0,0)(1,0,0),$ and $(0,1,0)(0,1,0)]$

Assume distances are in meters.