Help urgent maths

So Q moves in direction 3i - 4j (as it is parallel to p's movement) and has a fixed point of i - j . Another point that it gets to is 10i + cj.
Therefore, we can say that 10i +cj = i-j + a (3i - 4j) where a is a positive constant
Then match coefficients:
i: 10 = 1 + 3a --> a = 3
j: c = -1 - 4a
c = -1 - 4(3) = -13

But
3i - 4j is the acceleration, why do we add it on??

You've got 2 things going on here:

Q moves from i - j to 10i +cj, so its "direction of motion" is 9i +(c+1)j - just by subtracting one position vector from the other.

P is moving with constant acceleration 3i - 4j, so suvat says v = u + ta = t(3i - 4j) since it starts from rest. So P's "direction of motion" is just 3i - 4j.

"Parallel" means 9i + (c+1)j = k(3i - 4j) for some scalar k, So k = 3 and c + 1 = -12 giving c = -13 as required.

But
3i - 4j is the acceleration, why do we add it on??