Question

If the line joining $(2, 3, -1)$ and $(3, 5, -3)$ is perpendicular to the line joining $(1, 2, 3)$ and $(3, 5, \lambda)$, then $A =$

• A. $-3$
• B. $2$
• C. $5$
• D. $7$

Answer 1

Answer: (D)

$7$

Answer 2

$d$.$r??$ of the two lines are $1$, $2$, $-2$ and $2$, $3$, $\lambda - 3$. Since, lines are perpendicular $\therefore a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}=0$ $\Rightarrow 1\times2+2\times3-2\left(\lambda-3\right)=0$ $\Rightarrow \lambda=7$