Exercise 4.1.19

$L^{\text{⊥}}$ is the 2-dimensional subspace (a plane) in $R^3$ perpendicular to $L$. Then ${\left(L^{\text{⊥}}\right)}^{\text{⊥}}$ is a 1-dimensional subspace (a line) perpendicular to $L^{\text{⊥}}$. In fact ${\left(L^{\text{⊥}}\right)}^{\text{⊥}}$ is $L$.