Question

let z1=(1,0,1) ,z2=(0,1,-2) ,z3=(-1,-1,0) .
a. if z=(a,b.c), find f(z).
b. let f be a functional such that f(z1)=f(z2)=0 and f(z3) not equal to zero. if z=(2,3,-1) show that f(z) not equal to zero.