The line L_1 is parallel to the vector a =-3 i +2 j +4 k and passes through the point (7,6,2) and the line L_2 is parallel to the vector b =2 i + j…

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