The set of real values of $\lambda$ for which the vectors $\lambda \hat{i}-3 \hat{j}+5 \hat{k}$ and $2…
The set of real values of $\lambda$ for which the vectors $\lambda \hat{i}-3 \hat{j}+5 \hat{k}$ and $2 \lambda \hat{i}-\lambda \hat{j}+\hat{k}$ are perpendicular to each other is
$\{0,1\}$
$\{-2\}$
$\{2,-1\}$
$\phi$
Solution
$
\begin{aligned}
& (\lambda \hat{i}-3 \hat{j}+5 \hat{k}) \cdot(2 \lambda \hat{i}-\lambda \hat{j}+\hat{k})=0 \\
& \Rightarrow \quad 2 \lambda^2+3 \lambda+5=0 \\
&
\end{aligned}
$
as $D=9-40 < 0$, no real values of $\lambda$ satisty the equation