# Why do we say the resultant vector as the relative motion in this case?

If a car A moves with acceleration $$2m/s^2$$due east and car B moves $$1m/s^2$$due north. What would be the acceleration of car B with respect to car A. Now , for this. The solution in my textbook is that they just took the resultant. I don’t understand why would we take the resultant of the two vectors as the value for relative velocity $$a_{BA}$$.

• Acceleration is a vector quantity and thus follows vector laws. To car A, B will seem to accelerate west at 2 m/s^2 and accelerate north at 1m/s^2 which u add by pythagoras theorem. – LoneAcademic Mar 29 at 1:42
• Is there any method like “Minimum distance of approach “ used here ? @SarthakGirdhar – Srijan M.T Mar 29 at 1:45
• Maybe there is. I havent heard that term before. – LoneAcademic Mar 29 at 2:02

Since east and north are perpendicular to each other I would like to break it into $$i$$ and $$j$$
$$A_a$$=2i
$$A_b$$=1j
$$A_{b/a}=A_b-A_a$$