find a 3X3 projection matrix P such that Px is the projection of the
point x onto the plane x1+x2-x3 =0.

Let maxtrix P is:
/P11 P12 P13\
|P21 P22 P23|   
\P31 P32 P33/
      /X\
and x=|Y|
      \Z/

then Px is:
/P11x+P12y+P13Z\ /x1\
|P21x+P22y+P23z|=|x2|
\P31x+P32y+P33z/ \x2/

you need 
x1+x2-x3=0
P11x+P12y+P13z+P21x+P22y+P21z-P31x-P32y-P33z=0

x(P11+P21-P31)+ y(P12+P22-P32) +z(P13+P23-P33)=0
it is for every x,y and z so:
P11+P21-P31=0
P12+P22-P32=0
P13+P23-P33=0

You can select 2 fields in every column and then calculate last field
in column using this formula.