Let a =2 i -7 j +5 k, b = i + k and c = i +2 j -3 k be three given vectors. If r is a vector such that r × a = c × a and r · b =0, then | r | is…

Let $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{i}-7 \hat{j}+5 \hat{k}, \overrightarrow{\mathrm{~b}}=\hat{i}+\hat{k}$ and $\displaystyle \overrightarrow{\mathrm{c}}=\hat{i}+2 \hat{j}-3 \hat{k}$ be three given vectors. If $\displaystyle \overrightarrow{\mathrm{r}}$ is a vector such that $\displaystyle \vec{r} \times \vec{a}=\vec{c} \times \vec{a}$ and $\displaystyle \vec{r} \cdot \vec{b}=0$, then $\displaystyle |\vec{r}|$ is equal to: