Given a random vector X with the multivariate normal distribution F(X), we know that, for two vectors a and b, the projections $A=\sum_j a_j X_j $ and $B=\sum_i b_i X_i $ are univariate normal.
I'm interested in the joint distribution of A and B. Is their joint distribution normal? Is the dependence between A and B described only by their correlation? (do they have only linear dependence?) Thank you for any insight. References are highly appreciated as well.