Zadanie 12b, Paper 1, maj 2023, TZ1, Matematyka AA IB HL

Lines L_1,L_2 meet at P with acute angle π/3. A point A = (2t, 3t, 2) with t>0 lies on L_2, and $\overrightarrow{PA}=(2t,t+2,0)$. A direction vector of L_1 is d=(1,0,1). The plane Π contains both lines. A right circular cylinder has one base in Π, centred at A, with L_1 tangent to its circular boundary. The cylinder volume is $96\pi\sqrt3$ cubic units.