माना सदिश \(\overrightarrow{\mathrm{a}}=6 \hat{\mathrm{i}}+9 \hat{\mathrm{j}}+12 \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\alpha \hat{\mathrm{i}}+11 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\) तथा \(\overrightarrow{\mathrm{c}}\) इस प्रकार हैं कि \(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\) है। यदि \(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=-12, \overrightarrow{\mathrm{c}} \cdot(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}})=5\) हैं, तो \(\overrightarrow{\mathrm{c}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})\) बराबर है_________

1. A \(10\)
2. B \(11\)
3. C \(12\)
4. D \(13\)