[UPSC CSE 2018] Central Force Motion and Gravitation (Q83, 10+10=20M)

(i) If a particle of mass m is in a central force field f(r)\hat{r}, then show that its path must be a plane curve, where \hat{r} is a unit vector in the direction of position vector \vec{r}.

(ii) A block of mass m having negligible dimension is sliding freely in x-direction with velocity \vec{v}=v\hat{\imath} as shown in the diagram.

What is its angular momentum \vec{L}_O about origin O and its angular momentum \vec{L}_A about the point A on y-axis?