Vector Algebra

If \(\bar{a}=\hat{i}+4 \hat{j}+2 \hat{k}, \bar{b}=3 \hat{i}-2 \hat{j}+7 \hat{k}, \bar{c}=2 \hat{i}-\hat{j}+4 \hat{k}\), then a vector \(\overline{\mathrm{d}}\) which is parallel to vector \(\overline{\mathrm{a}} \times \overline{\mathrm{b}}\) and which \(\overline{\mathrm{c}} \cdot \overline{\mathrm{d}}=15\), is