A radar station tracks a jet fighter flying with constant speed. If the radar station is considered to be at the origin, the fighters starting position is 2i + 8j + k and 1 minute later it is at 8i - 4j + 13k. (therefore, velocity = 6i - 12j + 12k)
Find the point along the path where the fighter is closes to the station?
So far, I've found the velocity of the fighter and therefore the vector that describes its position at any time (using m), i.e.
(2 + 6m)i + (8 - 12m)j + (1 + 12m)k
I then used my CAS to find m when the dot product of
(2 + 6m)i + (8 - 12m)j + (1 + 12m)k . (0i + 0j + 0k) = 0 and solve for m, but I got no answer (only 'true').
I'm now lost for as how to solve this question, please help!