Let $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=7 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$. The vector $\mathbf{x}$ such that $\mathbf{x} \cdot \mathbf{c}=60$ and perpendicular to both $\mathbf{a}, \mathbf{b}$ is