I am struggling to solve this question. I have to find the set of lines through a fixed point in $\mathbb{P}^3$ using $Gr(2,4)$. How can I show that this set is inside $Gr(2,4)$ and a subset in $\mathbb{P}^5$ defined by three independent linear equations using Plücker coordinates?
Since I have only learned about basic algebraic geometry, I have tried to solve this by finding a corresponding variety lying on $\mathbb{A}^3$. However, I have no idea how to go further from here. Also, I'd like to approach this question only using Plücker coordinates.