Exercise 111.48.1. Let $k$ be a field. Let $X = \mathbf{P}^3_ k$. Let $L \subset X$ and $P \subset X$ be a line and a plane, viewed as closed subschemes cut out by $1$, resp., $2$ linear equations. Compute the dimensions of

for all $i$. Make sure to do both the case where $L$ is contained in $P$ and the case where $L$ is not contained in $P$.

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