mechanics vectors

my question is how to find p and q:

f1=(4i-5j) and f2=(pi+qj)
the resultant force, r=f1+f2 acts in a direction parallel to (3i-j)

i've added f1 and f2 together to get ((4+p)i+(-5+q)j) but that's as far as my brain has taken me.

As you've written it, you can't find p and q as such, only a linear relationship between the two. Can you post an image of the original question?

i realised after i posted this that i wasn't supposed to find p and q, i was just supposed to:

a) find the angle between R and vector i
b) show that p+3q=11
and c) find |R| if p=2

i can't put a photo up because i'm on my laptop rn, but sorry for the confusion

OK.

For two vectors to be parallel (including antiparallel - i.e. reverse direction), one will be a multiple of the other. There are a couple of way to look at it:

i) R = k(3i-j) for some unknown k. In particular, they will have the same i and j components, giving two equations, from which you can eliminate k.

ii) They both make the same angle to the i vector, for example, in particular the tan of that angle will be the same for each, giving you and equation to rearrange. I think part (a) is hinting you towards this methodology.