# Intersecting and Colliding Curves

#### Jason76

The particles don't collide because no value of t satisfies all three sets of parametric equations set equal to each other. Would the next step of seeing which points intersect involve solving the parametric equations for t?

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#### romsek

MHF Helper
what you have to realize is that the particles might not travel at the same rate.

So you can't just equate the components.

What you can do is let

$r_1(t)=<t, t^2, t^3>$

and

$r_2(s) = < 1+2s, 1+6s, 1+14s>$

and see if the 3 equations (each component) in two unknowns, $s$ and $t$, have a solution.

As it turns out there are 2 solutions, or points where the space curves intersect.

Colliding on the other hand requires that the two particles' paths intersect at a common time.

In this case you would just equate the components and as you saw there was no collision solution.

See if you can solve for the intersections.

1 person

#### Jason76

t = an s equation. That s equation is then plugged into the t^{2} equation. Next the equation is solved for s. The s values are plugged back into the s equations to get the points which are 1,1,1 and 2,4,8.

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