Points $P$ and $Q$ are given by $\overline{O P}=\bar{i}-\bar{j}-\bar{k}$ and $\overline{O Q}=-\bar{i}+\bar{j}+\bar{k}$. A line along the vector $\bar{a}=\bar{i}+\bar{j}$ passes through the point $P$ and another line along the vector $\bar{b}=\bar{j}-\bar{k}$ passes through the point $Q$. If a line along the vector $\bar{c}=\bar{i}-\bar{j}+\bar{k}$ intersects both the lines along the vectors $\bar{a}$ and $\bar{b}$ at $L$ and $M$ respectively, then $\overline{P M}=$

• A

  $\bar{i}-\bar{j}+2 \bar{k}$
• B

  $4 \bar{i}+4 \bar{j}$
• Correct answer
  C

  $-2 \bar{i}+10 \bar{j}-6 \bar{k}$
• D

  $3 \bar{i}-2 \bar{j}+\bar{k}$

Hence, the correct answer is option: 'C'.