How to find a vector parallel to a line?

[r_swayze]

How do I find the vector parallel to the line x+2 = 1/2y = z-3 ?

the book says its < 1,2,1 > but I have no idea how to get there?

 

[tiny-tim]

Hi r_swayze!

Just go for the obvious …

that line is parallel to the line x = 1/2y = z, from which it's pretty obvious that if you increase x by 1, the you increase y by 2, and z by 1

 

[r_swayze]

oh I think I see now, so the +2 and -3 from the x and z equations are just telling the shift in position?

 

[tiny-tim]

Yup!