Finding the vectorial element and surface area dS

[adichy]

Homework Statement

The domain D is a tetrahedron bounded by the planes x = 0, y = 0, z = 0 and
x + y + z = 1 Calculate
(a). The volume of the domain.
[10 marks]
(b). The x-coordinate of the centre-of-mass of the domain, assuming constant density.
[9 marks]
(c). Find, in terms of x and y the vector R from the origin to a point on the plane
x + y + z = 1.
[2 marks]
(d). Find the (vectorial) element of surface area dS on that plane, in terms of x, y, dx
and dy.
[4 marks]
(e). Hence calculate the area of the portion of that plane on the surface of the domain
D

Homework Equations

The Attempt at a Solution

ive done parts a and b
a)1/6 b)1/4
c)was slightly confused on what to do, can't seem to remember the exact method but i think vector R=[x,y,z],
most likely wrong since the question asked it to be in terms of x and y only.
d) Not completely confident with what you're meant to do here. My guess is find ds (it asked it to be in terms of x,y dx and dy but no dz, not sure how to get rid of it) and multiply it with the surface of the plane (problem with this 1 is i don't know what to multiply ds by as in i dnt kno what the surface is)
e) not exactly sure what the question is asking me to do

your help would be appreciated, thanks in advance ^^

 

[Mark44]

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[adichy]

sorry editted the post

 

[Mark44]

Thanks! And welcome to Physics Forums!

For part c, any point on the plane x + y + z = 1 will have the form (x, y, 1 - x - y), with x >= 0, y >= 0, and 1 - x - y >= 0.