The lines \vec{r}= (2\hat{i}-3\hat{j}+7\hat{k})+λ(2\hat{i}+p\hat{j}+5\hat{k}) and \vec{r}=(\hat{i}+2\hat{j}+3\hat{k}) + \mu (3\hat{i}+p\hat{j}+p\hat{k}) are perpendicular , if p =
Options:
-6, -1
-1, 6
2, 3
none of these
Correct Answer:
-1, 6
Explanation:
Given lines are parallel to the vectors \vec{b_1}=2\hat{i}+p\hat{j}+5\hat{k} and \vec{b_2}=3\hat{i}-p\hat{j}+p\hat{k} respectively.