The shortest distance between the skew lines\[{{l}_{1}}:\vec{r}={{\vec{a}}_{1}}+\lambda {{\vec{b}}_{1}}{{l}_{2}}:\vec{r}={{\vec{a}}_{2}}+\mu {{\vec{b}}_{2}}\] is

\[\frac{\left| ({{{\vec{a}}}_{2}}-{{{\vec{a}}}_{1}}).{{{\vec{a}}}_{2}}\times {{{\vec{b}}}_{2}} \right|}{\left| {{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}} \right|}\]

\[\frac{|({{{\vec{a}}}_{2}}-{{{\vec{a}}}_{1}}).{{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}}|}{|{{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}}|}\]

\[\frac{\left| ({{{\vec{a}}}_{2}}-{{{\vec{b}}}_{2}}).{{{\vec{a}}}_{1}}\times {{{\vec{b}}}_{1}} \right|}{\left| {{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}} \right|}\]

\[\frac{\left| ({{{\vec{a}}}_{1}}-{{{\vec{b}}}_{2}}).{{{\vec{b}}}_{1}}\times {{{\vec{a}}}_{2}} \right|}{\left| {{{\vec{b}}}_{1}}\times {{{\vec{a}}}_{2}} \right|}\]

The shortest distance between the skew lines\[{{l}_{1}}:\vec{r}={{\vec

1.	The shortest distance between the skew lines\[{{l}_{1}}:\vec{r}={{\vec{a}}_{1}}+\lambda {{\vec{b}}_{1}}{{l}_{2}}:\vec{r}={{\vec{a}}_{2}}+\mu {{\vec{b}}_{2}}\] is
A.	\[\frac{\|({{{\vec{a}}}_{2}}-{{{\vec{a}}}_{1}}).{{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}}\|}{\|{{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}}\|}\]
B.	\[\frac{\left\| ({{{\vec{a}}}_{2}}-{{{\vec{a}}}_{1}}).{{{\vec{a}}}_{2}}\times {{{\vec{b}}}_{2}} \right\|}{\left\| {{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}} \right\|}\]
C.	\[\frac{\left\| ({{{\vec{a}}}_{2}}-{{{\vec{b}}}_{2}}).{{{\vec{a}}}_{1}}\times {{{\vec{b}}}_{1}} \right\|}{\left\| {{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}} \right\|}\]
D.	\[\frac{\left\| ({{{\vec{a}}}_{1}}-{{{\vec{b}}}_{2}}).{{{\vec{b}}}_{1}}\times {{{\vec{a}}}_{2}} \right\|}{\left\| {{{\vec{b}}}_{1}}\times {{{\vec{a}}}_{2}} \right\|}\]
Answer» B. \[\frac{\left\| ({{{\vec{a}}}_{2}}-{{{\vec{a}}}_{1}}).{{{\vec{a}}}_{2}}\times {{{\vec{b}}}_{2}} \right\|}{\left\| {{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}} \right\|}\]

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