I'm having trouble with this question:
A particle moves so that its position vector with respect to the origin $O$ of a reference frame $Oxyz$ is $$ \mathbf{r}(t)=bcos(wt) \mathbf{e}_1+bsin(wt)\mathbf{e}_2+Vt\mathbf{e}_3$$ Where $\mathbf{e}_1,\mathbf{e}_2,\mathbf{e}_3$ are unit vectors parallel to the axis $Ox,Oy,Oz$ ; $b,w,V$ are positive constants. (i) Find the velocity and speed of the particle
(ii) Prove that the particle moves on a circular cylinder, whose axis is $Oz$
(iii) Find the particle's acceleration, and indicate its direction in a diagram.
Part (i) is simple enough, differentiating $\mathbf{r}(t)$ gives $\mathbf{v}(t)$ so $$\mathbf{v}(t)=-bwsin(wt)\mathbf{e}_1+bwcos(wt)\mathbf{e}_2+V\mathbf{e}_3$$ And therefore the speed is $$|v|=\sqrt{b^2w^2+V^2}$$ Part (iii) uses the same technique.I.e the acceleration will be towards the centre of the circle in $OxOy$ as there is no $z$ component. However I'm stuck on part (ii), as I'm not sure what constitutes a proof in this case. Is it enough to say that the particle is moving in a circle radius ${b}$ in the $OxOy$ and linearing increasing in $Oz$. Therefore it would map a helix around a circular cylinder which would have its axis at $Oz$? Or do I have to construct an algebraic interpretation, I'm just a little confused.
Thanks
