I'm trying to prove that given 3 disjoint lines in $\mathbb{P}^{3}$ there exists a non-singular quadric containing them. The exercise is from the following link:
http://www.uam.es/personal_pdi/ciencias/abenito/varios/ReidAlgebraicGeometry.pdf
I think you have to use page 19 of the source and make an argument based on dimension, but I'm really not sure. Any hint/help appreciated.