$R$ is not reflexive, as a line $L_{1}$ can not be perpendicular to itself, i.e., $\left(L_{1}, \,L_{1}\right)$ $\notin R$. $R$ is symmetric as $\left(L_{1}, L_{2}\right) \in R$

$\Rightarrow $          $L_{1}$ is perpendicular to $L_{2}$

$\Rightarrow $          $L_{2}$ is perpendicular to $L_{1}$

$\Rightarrow  $          $\left(L_{2},\, L_{1}\right) \in R$

$R$ is not transitive. Indeed, if $L_{1}$ is perpendicular to $L_{2}$ and $L _{2}$ is perpendicular to $L _{3},$ then $L _{1}$ can never be perpendicular to $L _{3} .$ In fact, $L _{1}$ is parallel to $L _{3},$ ie., $\left( L _{1},\, L _{2}\right) \in R ,\left( L _{2}, L _{3}\right) \in R$ but $\left( L _{1}, L _{3}\right) \notin R$.