For every line $l$ in $\mathbb{R}^3$ we write $l^\perp$ for the plane orthogonal to $l$. Let $F$ be : $F = \{(u,l) | l\in\mathbb{P}^2(\mathbb{R}),u\in l^\perp\}$
How do you show that this is not isomorphic to the trivial bundle on $\mathbb{P}^2(\mathbb{R})$.