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The shortest distance between the lines $ \overrightarrow {r}=3\overrightarrow {i}+5 \overrightarrow {j}+ 7 \overrightarrow {k}+ \lambda (\overrightarrow {i}+2 \overrightarrow {j}+\overrightarrow {k})$ and $\overrightarrow {r}=- \overrightarrow {i} -\overrightarrow {j} -\overrightarrow {k}+ \mu (7\overrightarrow {i}-6 \overrightarrow {j}+\overrightarrow {k}) $ is

\[(a)\;\frac{16}{5 \sqrt 5} \quad (b)\;\frac{26}{5 \sqrt 5} \quad (c)\;\frac{36}{5 \sqrt 5} \quad (d)\;\frac{46}{5 \sqrt 5} \]

1 Answer

$(d)\;\frac{46}{5 \sqrt 5}$
answered Nov 7, 2013 by pady_1
 

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