Show that the points A(-9,-3,-16) and B(6,2,14) lie on the line that passes through (0,0,2) and has direction numbers (3,1,6). Describe the line segment from A to B using parametric equations with suitable restrictions on the parameter.

I need help with the end of part B)

Describe the line segment from A to B using parametric equations with suitable restrictions on the parameter.

so I found the parametric equations which are:

x=3t, y=t,z=2+6t

But I am having trouble finding their answer of -3<=t<=2 for the restriction.

How did they find this?

I will add part a if it helps:

d=AB=(15,5,30)

d=(3,1,6)

sym eqtn

x/3

y/1

(z-2)/6

sub in point (0,0,2)

0=0=0 therefore point lies on line

Ok, so how did they get the restriction on t? thanks for your help!