question_answer

Line \[{{L}_{1}}\] is parallel to vector \[\vec{\alpha }=-\,3\hat{i}+2\hat{j}+4\hat{k}\] and passes through a point A (7, 6, 2) and line \[{{L}_{2}}\] is parallel to a vector \[\vec{\beta }=2\hat{i}+\hat{j}+3\hat{k}\] and passes through a point B (5, 3, 4). Now a line \[{{L}_{3}}\] parallel to a vector \[\vec{r}=2\hat{i}-2\hat{j}-\hat{k}\] intersects the lines \[{{L}_{1}}\] and \[{{L}_{2}}\] at points C and D respectively, then \[\left| \overrightarrow{CD} \right|\] is equal to

A) 7                                 

B) 8

C) 9

D) none of these