The paths of two aeroplanes in an aerial display are simultaneously defined by the vectors:
r1(t) = (16 - 3t)i + tj + (3 + 2t)k
r2(t) = (3 + 2t)i + (1 + t)j + (11 - t)k
t represents time in minutes. Find:
a) the position vector of the first plane after one minute.
r1(1) = 13i + j + 5k
b) the unit vectors parallel to the flights of each of the two planes
The inclusion of t has thrown me off.
c) the acute angle between their lines of flight, correct to two decimal places
d) the point at which their two paths cross
I can do this for vectors in two dimensions, but not three.
e) the vector which represents the displacement between the two planes after t seconds
If you could walk me through this question, that would be great. Bear in mind that most of this is new to me.