A) \[2\sqrt{30}\]
B) \[\frac{7}{2}\sqrt{30}\]
C) \[3\sqrt{30}\]
D) 3
Correct Answer: C
Solution :
[c] Shortest distance \[=\left| \frac{[{{{\vec{a}}}_{2}}-{{{\vec{a}}}_{1}}{{{\vec{b}}}_{1}}{{{\vec{b}}}_{2}}]}{\left| {{{\vec{b}}}_{1}}\times {{b}_{2}} \right|} \right|\] \[{{\vec{b}}_{1}}\times {{\vec{b}}_{2}}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 3 & -2 & 1 \\ -3 & 2 & 4 \\ \end{matrix} \right|=-6\hat{i}-15\hat{j}+3\hat{k}\] \[\left| {{{\vec{b}}}_{1}}\times {{{\vec{b}}}_{2}} \right|=\sqrt{36+225+9}=\sqrt{270}\] and \[\left[ {{{\vec{a}}}_{2}}-{{{\vec{a}}}_{1}}{{{\vec{b}}}_{1}}{{{\vec{b}}}_{2}} \right]=-36-225-9=-270\] \[\Rightarrow \] Shortest distance \[=\sqrt{270}=3\sqrt{30}\]
You need to login to perform this action.
You will be redirected in
3 sec
