Symmetric Matrices & Quadratic Forms · Medium problem

Let $\mathbf v_1 = (1, 1, 0)$ and $\mathbf v_2 = (0, 1, 1)$. The quadratic form $q(a, b) = |a\mathbf v_1 + b\mathbf v_2|^2$ can be written $\begin{pmatrix}a & b\end{pmatrix}G\begin{pmatrix}a\\b\end{pmatrix}$ with $G$ symmetric. Find $\det G$.