question_answer

If a line \[I\] passing through the origin is perpendicular to the lines

\[{{I}_{1}}:(3+t)\,\,\hat{i}+(-1+2t)\,\,\hat{j}+(4+2t)\,\,\hat{k},\] \[-\infty <t<\infty \]

\[{{I}_{2}}:(3+2s)\,\,\hat{i}+(3+2s)\,\,\hat{j}+(2+s)\,\,\hat{k},\]  \[-\infty <s<\infty \]

Then, the coordinates of the point on \[{{I}_{2}}\] at a distance of \[\sqrt{17}\] from the point of intersection of I and \[{{I}_{2}}\] are ________.

A)  \[\left( \frac{7}{9},\,\,\frac{8}{9},\,\,\frac{8}{9} \right)\] and \[(1,-1,0)\] 

B)  \[\left( \frac{7}{9},\,\,\frac{7}{9},\,\,\frac{8}{9} \right)\] and \[(-1,-1,0)\]

C)  \[\left( \frac{7}{3},\,\,\frac{7}{3},\,\,\frac{5}{3} \right)\]and \[(-1,-1,0)\]

D)  \[\left( \frac{7}{3},\,\,\frac{7}{3},\,\,\frac{5}{3} \right)\]and \[(1,-1,0)\]

E)  None of these