The question asks for the vector equation for the line of intersection by the planes x+2y-2z=5 and 6x-3y+2z=8

Answer is given as

But when I do the working

Labeling x+2y-2z=5 as equation 1

and 6x-3y+2z=8 as equation 2

Multiply equation 1 by 6 to get 6x+12y-12z=30 call this equation 3

equation 2 minus equation 3 to get

Let z=t

Than from equation 1

and so

Am I right with my negative signs in <-2,-14,15>

and the answer in the text of <2,14,15> is wrong?