Distribution of $X_3$ given that $X_1 + X_2 =1$ for $(X_1,X_2,X_3)$ centered gaussian with given covariance matrix

Question

Let $X=(X_1,X_2,X_3)$ have a multivariate normal distribution with $EX_1 = EX_2 = EX_3 = 0$ and covariance matrix:

$ \left( \begin{array}{ccc} 2 & -1 & 1 \\ -1 & 5 & 0 \\ 1 & 0 & 3 \end{array} \right) $

Determine the distribution of $X_3$ given that $X_1 + X_2 =1$

I have a hard time finding examples like this one so I don't know how to deal with them. Some basic explanation would be appreciate if possible. :)