Two lines have vector equations _1: r= 1 2 -1 +lambda 2 -1 3 and _2: r= 5 0 5 +mu -4 2 -6, where lam

Question

Two lines have vector equations _1: r= 1 2 -1 +lambda 2 -1 3 and _2: r= 5 0 5 +mu -4 2 -6, where lambda,mu in R. - Show that the two lines coincide, and find the relation between lambda and mu for the same point. Two particles P and Q start moving at time t=0. Their position vectors at time t 0 seconds are given by the equations of _1 and _2, respectively, with lambda=t and mu=t. Position coordinates are measured in metres. - Find the speed of each particle. - Determine whether the particles collide. If they do, find the time and position of collision.

Accepted Answer

$\lambda=2-2\mu$; speeds $\sqrt{14}$ and $2\sqrt{14}\text{ m s}^{-1}$; collision at $t=\frac23\text{ s}$, position $(\frac73,\frac43,1)$.

Coincident paths and a collision

Coincident paths and a collision

Solution:

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