A) 1
B) \[\frac{1}{2}\]
C) \[\frac{3}{4}\]
D) \[17\]
E) \[0\]
Correct Answer: E
Solution :
On comparing the given lines with \[\overrightarrow{r}=\overrightarrow{a}+t\overrightarrow{c}\]and\[\overrightarrow{r}=\overrightarrow{b}+s\overrightarrow{d}\] We get, \[\overrightarrow{a}=(4\hat{i}-7\hat{i}-9\hat{k}),\overrightarrow{c}=3\hat{i}-7\hat{j}+4\hat{k}\] \[\overrightarrow{b}=7\hat{i}-14\hat{j}-5\hat{k},\overrightarrow{d}=-3\hat{i}+7\hat{j}-4\hat{k}\] Now, \[[\overrightarrow{a}-\overrightarrow{b}\overrightarrow{c}\overrightarrow{d}]=\left| \begin{matrix} -3 & 7 & -4 \\ 3 & -7 & 4 \\ -3 & 7 & -4 \\ \end{matrix} \right|\] \[=0\] (\[\because \]two rows are identical) \[\therefore \] Shortest distance\[=\frac{[\overrightarrow{a}-\overrightarrow{b}\overrightarrow{c}\overrightarrow{d}]}{[\overrightarrow{c}\times \overrightarrow{d}]}\] \[=0\]You need to login to perform this action.
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