Given a field $F$ and $A = F^3$. we define $L$ to be the line that goes through the points: $(8,1,-1)$, $(5,0,-1)$. My object is to find two polynomials $q(X_1,X_2,X_3)$, $p(X_1,X_2,X_3)$ in $F[X_1,X_2,X_3]$ of degree $\leq 1$ such that $L$ is the set of zeros of $p$ and $q$.
thanks. benny