If two objects travel through space along two different curves

PHYSICS · Subjective · AP · Physics C: Mechanics · Kinematics · Kinematics

Problem

If two objects travel through space along two different curves, it's often important to know whether they will collide. Two particles travel along the space curves r1(t)=⟨t,t2,t3⟩r2(t)=⟨1+2t,1+6t,1+14t⟩\mathbf{r}_1(t) = \langle t, t^2, t^3 \rangle \quad \mathbf{r}_2(t) = \langle 1 + 2t, 1 + 6t, 1 + 14t \rangle Do the particles collide? Do their paths intersect?

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