Hi,

I have a couple of questions...

1) How would you use vector methods to prove that in the parallelogram OABC, the line drawn from O to the mid-point of AB cuts AC at the point of trisection of AC that is nearer to A.

2) A defensive missile battery launches a ground to air missile A to intercept an incoming enemy missile B. At the moment of A's launch the position vectors of A and B (in meters), relative to the command HQ were:

r_{A}= <600, 0, 0> & r_{B}= <2200, 4000, 600>

A and B maintain the velocities (m/s): v_{A}= <-196, 213, 18> & v_{B}= <-240, 100, 0>

Prove that A will not intercept B and find "how much it misses by".

Suppose instead that the computer on missile A detects that its off target and, 20 sec into its flight, A changes its velocity and interception occurs after a further 15 sec. Find the constant velocity that A must maintain during this final 15 sec for interception to occur.

Sorry that it's really long... Thank you in advance!