JEE Math Practice Question

The line $\mathrm{L}_1$ is parallel to the vector $\overrightarrow{\mathrm{a}}=-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and passes through the point $(7,6,2)$ and the line $\mathrm{L}_2$ is parallel to the vector $\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}+3 \hat{k}$ and passes through the point $(5,3,4)$. The shortest distance between the lines $L_1$ and $L_2$ is :

1. A.$\frac{23}{\sqrt{38}}$
2. B.$\frac{21}{\sqrt{38}}$
3. C.$\frac{23}{\sqrt{57}}$
4. D.$\frac{21}{\sqrt{57}}$