A) \[-4\hat{i}+5\hat{j}+11\hat{k}\]
B) \[4\hat{i}+5\hat{j}+11\hat{k}\]
C) \[-4\hat{i}-5\hat{j}+11\hat{k}\]
D) \[-4\hat{i}+5\hat{j}-11\hat{k}\]
Correct Answer: B
Solution :
Given planes are \[\vec{r}.(\hat{i}-3\hat{j}+\hat{k})=1\] ?.(i) and \[\vec{r}.(2\hat{i}+5\hat{j}-3\hat{k})=2\] ?..(ii) Now, \[(\hat{i}-3\hat{j}+\hat{k})\times (2\hat{i}+5\hat{j}-3\hat{k})\] \[=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & -3 & 1 \\ 2 & 5 & -3 \\ \end{matrix} \right|\] \[=\hat{i}(9-5)-\hat{j}(-3-2)+\hat{k}(5+6)\] \[=4\hat{i}+5\hat{j}+11\hat{k}\] So, line of intersection of the planes is parallel to the vector \[4\hat{i}+5\hat{j}+11\hat{k}\].
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