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 =
Answer & explanation
Correct answer: option 2
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.
If the lines are perpendicular , then
$\vec{p_1}.\vec{p_2}= 0 ⇒ 6 - p^2 + 5p = 0 ⇒ p = -1, 6 $