Question

Find the value of $\lambda$ if two lines having direction ratios $1,-2,3$ and $2-\lambda ,1+\lambda ,-\lambda$ are perpendicular to each other

• A. $1$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

Answer: (C)

$0$

For a given lines to be perpendicular is:

$\begin{array}{c}{a}_1{a}_2+b_1{b}_2+c_1{c}_2=0\\ \Rightarrow \left(1+\left(2-\lambda \right)\right)+\left(-2\right)\left(1+\lambda \right)+3\left(-\lambda \right)=0\\ \Rightarrow 2-\lambda -2-2\lambda -3\lambda =0\\ \Rightarrow -6\lambda =0\\ \Rightarrow \lambda =0\end{array}$

Hence, the correct option is $\left(C\right)$