माना तीन सदिश \(\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{k}}\) तथा \(\overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}\) हैं। यदि एक सदिश \(\overrightarrow{\mathrm{r}}\) के लिए \(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}}\) तथा \(\overrightarrow r \cdot \overrightarrow{\mathrm{b}}=0\) हैं, तो \(|\overrightarrow{\mathrm{r}}|\) बराबर:

1. A \(\frac{11}{7} \sqrt{2}\)
2. B \(\frac{11}{7}\)
3. C \(\frac{11}{5} \sqrt{2}\)
4. D \(\frac{\sqrt{914}}{7}\)