Originally Posted by

**outlaw** At 12 noon the position vectors **r **and the velocity vectors **v** of two ships A and B are

**r**A = (2**i**+**j**)km **v**A = (3**i**+**j**)kmh^-1

**r**B = (-**i-**4**j**)km **v**B = (11**i**+3**j**)kmh^-1

(a) Show that at time *t* h after noon the position vector of B relative to A is given by:

[(8*t*-3)**i**+(2*t*-5)**j**]km

(b) Show that the distance *d* km between the vessels, at this time, is given by

*d*^2=68[*t*^2 - *t*+1/2]

(c) Hence show that the ships are nearest together at 12.30 p.m and find the distance between them at this time.