The paths of two aeroplanes in an aerial display are simultaneously defined by the vectors:

r_{1}(t) = (16 - 3t)i+ tj+ (3 + 2t)kr

_{2}(t) = (3 + 2t)i+ (1 + t)j+ (11 - t)k

trepresents time in minutes. Find:

a) the position vector of the first plane after one minute.

r_{1}(1) = 13i+j+ 5k

b) the unit vectors parallel to the flights of each of the two planes

The inclusion ofthas 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 aftertseconds

If you could walk me through this question, that would be great. Bear in mind that most of this is new to me.

Thanks.