Let the line L_1 be parallel to the vector -3 i +2 j +4 k and pass through the point ( 2,6,7 ), and the line L_2 be parallel to the vector 2 i + j +3…

Let the line $\displaystyle \mathrm{L}_1$ be parallel to the vector $\displaystyle -3 \hat{i}+2 \hat{j}+4 \hat{k}$ and pass through the point ( $\displaystyle 2,6,7$ ), and the line $\displaystyle \mathrm{L}_2$ be parallel to the vector $\displaystyle 2 \hat{i}+\hat{j}+3 \hat{k}$ and pass through the point ($\displaystyle 4$, $\displaystyle 3$, $\displaystyle 5$). If the line $\displaystyle \mathrm{L}_3$ is parallel to the vector $\displaystyle -3 \hat{i}+5 \hat{j}+16 \hat{k}$ and intersects the lines $\displaystyle \mathrm{L}_1$ and $\displaystyle \mathrm{L}_2$ at the points C and D, respectively, then $\displaystyle |\overrightarrow{\mathrm{CD}}|^2$ is equal to :