I'll assume your given vectors are in a 3x2 matrix called columnVectors, that your angles are in degrees, and that rotations are done in Z first and Y second.
Rz=@(x) [cosd(x),-sind(x),0 ; ...
sind(x),cosd(x),0 ;...
0 0 1];
Ry = @(x) [cosd(x), 0, sind(x); 0 1 0; -sind(x), 0, cosd(x) ];
R=Ry(beta)*Rz(alpha); %ANGLES ARE IN DEGREES!!
[XpYp,XpZp,YpZp]=deal(R.'*columnVectors);
XpYp(3,:)=0; %X'Y'
XpZp(2,:)=0; %X'Z'
YpZp(1,:)=0; %Y'Z'
XpYp=R*XpYp;
XpZp=R*XpZp;
YpZp=R*YpZp;
