If two objects travel through space along two different curves

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

If two objects travel through space along two different curves, it's often important to know whether they will collide. The trajectories of two particles are given by the vector functions r1(t)=⟨t2,7t−12,t2⟩r2(t)=⟨4t−3,t2,5t−6⟩\mathbf{r}_1(t) = \langle t^2, 7t - 12, t^2 \rangle \quad \mathbf{r}_2(t) = \langle 4t - 3, t^2, 5t - 6 \rangle for t≥0t \ge 0. Do the particles collide?

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