Quadratic forms of a singular multivariate normal

Let $X = (X_1, X_2, X_3)^T$ be a 3-dimensional random vector having multivariate normal distribution with mean vector $(0,0,0)^T$ and covariance matrix $\Sigma = \begin{pmatrix} 4 & 0 & 0 \ 0 & 9 & 0 \ 0 & 0 & 4 \end{pmatrix}$. Let $\alpha^T = (2, 0, -1)$ and $\beta^T = (1, 1, 1)$. Then which of the following statements is/are correct?