(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two particles are moving on trajectories given by r=a+ut and r=b+vt respectively where a, b, u and v are constant vectors and t is the time. Show that the particles will collide if v.(bxu)=v.(axu) Obtain an expression for the time of the collision in terms of a, b, u and v. (I think I've done the parts so far.) Hence, or otherwise, show that the collision will take place at position r=b+((a.(bxu))/(v.(bxu))v

2. Relevant equations

If three vectors a, b, c are linearly dependent, a.(bxc)=o

3. The attempt at a solution

a+ut=b+vt

ut=(b-a)+vt

ut, vt, and b-a are coplanar. Since t is a scalar multiple, u, v, and b-a are coplanar.

v.((b-a)xu)=0

v.(bxu-axu)=o

v.(bxu)=v.(axu)

ut-vt=b-a

(u-v)t=b-a

t=mod(b-a)/mod(u-v)

I can't see how this expression for to is equivalent to ((a.(bxu))/(v.(bxu)), so I'm stuck.

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# Homework Help: Collision problem using vectors

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