MCQ
The line $L_{1}$ is parallel to the vector $\overrightarrow{\mathrm{a}}=-3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ and passes through the point $(7,6,2)$ and the line $L_{2}$ is parallel to the vector $\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and passes through the point $(5,3,4)$. The shortest distance between the lines $L_{1}$ and $L_{2}$ is :
- A$\frac{23}{\sqrt{38}}$
- B$\frac{21}{\sqrt{57}}$
- C$\frac{23}{\sqrt{57}}$
- D$\frac{21}{\sqrt{38}}$