Vector functions traveling along space curves

[aesailor]

Homework Statement

two particles travel along the space curves r₁(t)=<t, t², t³> r₂=<1+2t, 1+6t, 1+14t>
Do the particles collide? Do their paths intersect?

2. Homework Equations

if vector r(t)=<f(t), g(t), h(t)>, then
lim r(t) _t-->a = <lim f(t)_t-->a, lim g(t)_t-->a, lim h(t)_t-->a> provided the limits of the component functions exist.

The Attempt at a Solution

Vector r₂ passes through the point (1, 1, 1) and is parallel to the vector <2, 6, 14> which I do not believe is going to be parallel to vector r₁. I know that r₁ passes through the origin though.

 

[arkajad]

Start with this: never in your problem it is said that t is time. It is important to know whether t is a common time or just a parameter. Suppose it is time. Then they collide if there is t such that both are at the same place: r1(t)=r2(t). Their trajectories intersect if there is place in space that is visited by both particles, perhaps at different time for each particle: r1(t1)=r2(t2). Now draw it, imagine, and think what to do next.