maths a level general mechanics question

so im having difficulty understanding when to use i and j notation . and when to use the magnitude of these values. for example .


Relative to a fixed origin O , the horizontal unit vectors i and j are pointing due east
and due north, respectively.
A particle P , of mass 2 kg , is moving under the action of a single constant force F N. When t=0s, the velocity of P is (3i−5j)ms−1 and when t=4 the velocity
of P is (11i+7j)ms−1.

b) Determine the vector F.

in the mark scheme they used i and j in the v = u +at formula . however I calculated the magnitudes and got the wrong value . so when would I know to use i and j notation