Here's a way to do this without vectors:
plane equation: ax+by+cz=8
substituting x=0, y=1, and z=1 into the plane's equation:
a(0)+b(1)+c(1)=8
b+c=8
substituting the other two points in the same way:
a+b=8 ==> -a-b=-8
a+3c=8
add up these three equations:
b+c=8
-a-b=-8
a+3c=8
and you get:
(b+c)+(-a-b)+(a+3c)=(8)+(-8)+(8)
b+c-a-b+a+3c=8-8+8
(a-a)+(b-b)+(c+3c)=0+8
4c=8
c=2
b+c=8, and c=2, so b+2=8
b=6
a+b=8, and b=6, so a+6=8
a=2
therefore, the answer is (a, b, c) = (2, 6, 2)