how and when we will use i,j,k unit vector in 2d, and 3d

if there are only 2 unit vectors then it is a 2d problem.

if all three are present then it is 3d problem...

solve all dimensions differently

for example if it is 5i+4j position and the force applied is 10i+10j+10k then also object will move in 2d because j is not present in position vector and hence we will solve x direction and y direction separately using formula..

like if answer is good...