Here, for part c the context of this question suggests that you should have done part b which I assume you have done and I reckon the vector you got should be
,
. How that we got the base with us we now will focus on this part of the vector
. Note since we want the vector to be perpendicular and go through v we are going to have to find a dot product that leads to 0. However, we as mathematicians inherently like to make things easier for ourselves at times and to do so we will treat the z coordinate as 0. So now the z-coordinate 1 in
is merely a spectator because
The rest shall be "left as an exercise for the reader."