Conditional expectation for multivariate normal distribution

Question

Assume $\mathbf{X}=[X_1,X_2,X_3]$ follows a multivariate normal distribution, $\mathbf{X}\sim N_3 (\mu,\Sigma)$, where $\text{cov}(X_i,X_j)\neq 0$, for $i\neq j$. What is $\mathbb{E}[X_1 X_2|a_1X_1+a_2X_2+a_3 X_3>t]$ for any arbitrary number $a_i,t\in \mathbb{R}$?