Let a =2 i - j +5 k and b =α i +β j +2 k. If (( a × b ) × i ) · k =23/2, then | b × 2 j | is equal to

Let $\displaystyle \vec{a}=2 \hat{i}-\hat{j}+5 \hat{k}$ and $\displaystyle \vec{b}=\alpha \hat{i}+\beta \hat{j}+2 \hat{k}$. If $\displaystyle ((\vec{a} \times \vec{b}) \times \hat{i}) \cdot \hat{k}=\frac{23}{2}$, then $\displaystyle |\vec{b} \times 2 \hat{j}|$ is equal to