Two particles travel along the space curves
r1(t)=<t, t2, t3>, r2(t)=<1+2t, 1+6t, 1+14t>
Do the particles collide? Do their paths intersect?
I know how to find out how the particles collide, just set the corresponding components of both vectors equal to one another and look for a t-value that works for all of them (which there isn't). My question is how do you determine if their paths intersect?
Use the parametric equations
to sketch the curve by hand as viewed from above, with gaps indicating where the curve passes over itself. Start by showing that the projection of the curve onto the xy-plane has polar coordinates r=2+cos(1.5t) and Θ=t, so r varies between 1 and 3. Then show that z has maximum and minimum values when the projection is halfway between r=1 and r=3.