Question

Two ants, red ant and black ant, creeping along lines in 3-space. At time t, red ant is at point on the line

Answer 1

A. The distance between the red ant and the black ant is five units.

To represent the red ant,
xr = 3 - t 
yr = 2 + 2 t 
zr = 6 + 2 t 

To represent the black ant, 
xb = t/2 
yb = 2 + 3 t 
zb = 2 + t 

To calculate,
at t = 0 
xb - xr = -3 
yb - yr - 2-2 = 0 
zb - zr = 2-6 = -4 
Therefore,
d = √(9+16) = √(25) = 5

b. There will be no collision between the two ants.

To calculate,
3 - t = t/2
6 - 2t = t
6 = 3t
t = 2 

If t = 2,
2 + 2*2 = 2 + 3*2