Hi I'm trying to figure out how to do this question
$\ S={(x,y,z):x,y,z≥0, 2x+y+2z=4}, $ which is a surface in the first octant.
Find the equation of the line segment where S intersects the x-y plane. And then evaluate
$$\int_S (x +y + z) \;\mathrm{d}S $$
So I know that seeing as it's the xy-plane that means z = 0 so when I manipulate the equation to get y = 4-2x but I'm unsure how to do the rest especially the parameterisation (I'm quite new at this)
Help would be greatly appreciated
UPDATE : so I've found the points $\ (x, y, 2-x- \frac y2) $
when I differentiate this with respect to x I get $\ (1, 0, -1) $
when I differentiate this with respect to y I get $\ (0, 1,- \frac 12) $
if i take the cross product of both of these I get $\ (1, \frac 12, 1) $
So is that my answer?