Vector Algebra

Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=2 \hat{i}+4 \hat{j}-5 \hat{k}\) and \(\vec{c}=x \hat{i}+2 \hat{j}+3 \hat{k}, x \in \mathbb{R}\).
If \(\vec{d}\) is the unit vector in the direction of \(\vec{b}+\vec{c}\) such that \(\vec{a} \cdot \vec{d}=1\), then \((\vec{a} \times \vec{b}) \cdot \vec{c}\) is equal to