The lines \(\vec{r} = (\hat{\imath}+2\hat{\jmath}-\hat{k})+\lambda(2\hat{\imath}+p\hat{\jmath}+3\hat{k})\) and \(\vec{r} = (3\hat{\imath}-\hat{k})+\mu(5\hat{\imath}+2\hat{\jmath}-4\hat{k})\) are perpendicular to each other. The value of p is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1
Two lines \(\vec{r} = \vec{a}_1+\lambda\vec{b}_1\) and \(\vec{r} = \vec{a}_2+\mu\vec{b}_2\) are perpendicular when \(\vec{b}_1\cdot\vec{b}_2 = 0\). The points \(\vec{a}_1, \vec{a}_2\) play no part.
\((2)(5)+(p)(2)+(3)(-4) = 0\)
\(10+2p-12 = 0\)
\(2p = 2\)
\(p = 1\)