Let \(\mathbb K\) be a field of characteristic zero and let \(R = \mathbb K[x_1,\dots,x_k]\). Let \(\Sigma = \{ \ell_1,\dots,\ell_s\}\), where \(\ell_1,\dots,\ell_s\) are linear forms in \(R\), and we allow the possibility that some are proportional. Let \(s = |\Sigma|\). Define the ideal generated by \(a\)-fold products of \(\Sigma\) to be \(I_a(\Sigma) = \langle \ell_{i_1} \cdots \ell_{i_a} \ | \ 1 \leq i_1 < \dots < i_a \leq s \rangle\). We make the convention that \(I_0(\Sigma) = R\) and \(I_b(\Sigma) = 0\) for all \(b > s\). A conjecture of the author with Tohǎneanu and Xie states that the ideals generated by \(a\)-fold products of linear forms are of fiber type. Those authors proved it in the case of line arrangements in \(\mathbb P^2\) when \(a = |\Sigma |-2\). This conjecture was also verified by Garrousian, Simis and Tohǎneanu when \(\Sigma\) defines a hyperplane arrangement \(\mathcal A\) and \(a = |\mathcal A | - 1\). In this paper the author proves this conjecture in the case where \(\Sigma\) defines a hyperplane arrangement, \(\mathcal A\), in \(\mathbb P^{k-1}\) (so the linear forms are not proportional), with the additional assumption \(|\mathcal A | - a \geq k\). In this paper the author also proves a conjecture of Mantero, Miranda-Neto and Nagel on symbolic powers of ideals in the special case where the ideals are generated by \((|\mathcal A|-1)\)-fold products of linear forms and \(\mathcal A\) is a generic hyperplane arrangement.