A force F has magnitude of 15 N. Direction of F is at 37° from negative x-axis towards positive y-axis. Represent F in terms of i^ and j^.

The given force is as shown in figure. Let us find its x and y components.Fx=Fcos37°=15×45=12 N (along negative x-axis)Fy=Fsin37°=15×35=9 N (along positive y-axis)From parallelogram law of vector addition, we can see thatF=OM+ON=Fx(-i^)+Fy(j^)=(-12i^+9j^)N