I have this question and I'm not entirely sure how to go about it. I understand how to go about the problem in the projective space $\mathbb{P}2$: if I have two lines $l1$ and $l2$, then their intersection will be at a point $x$ such that: $$ l_1 = (a_1, b_1, c_!)^T \\ l_2 = (a_2, b_2, c_2)^T \\ l_1 \times l_2 = x $$
However, I am unsure how to translate this problem to the projective space $\mathbb{P}3$.
Adding onto this, how would I go about finding the line joining two points $x_1$ and $x_2$ in $\mathbb{P}3$? Would it be the same as finding the point of intersection as above?
Any help, links to resources exploring the problem would be appreciated. Thanks in advance!