Vector Algebra

If \(\hat{\mathbf{i}}+4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), and \(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) are position vectors of \(A, B\) and \(C\) respectively and if \(D\) and \(E\) are mid points of sides \(B C\) and \(A C\), then \(\mathbf{D E}\) is equal to