Explain relative velocity of man with respect to rain?

Concept. For rain problem, If ##vecV_A and vecV_B## are velocities of objects ##A and B## respectively then

##vecV_(AB)=vecV_A-vecV_B## is the velocity of ##A## with respect to ##B##.

Following the above logic

##vecV_(rm)=vecV_r -vecV_m## is velocity of rain with respect to man.

See the vector representation on the right side of the figure above.

1. Velocity vectors ##vecV_m and vec V_r## are drawn.
2. Recall ##-ve## sign in front of the the second term. Therefore, draw ##-vecV_m## at the tip of ##vecV_r##
3. Join the tail of ##vecV_r## to the tip of ##-vecV_m## to obtain ##vecV_(rm)## as velocity of rain with respect to man.

Similar steps need to be followed if ##vecV_(mr)##, velocity of man with respect to rain is to be found.

1. Velocity vectors ##vecV_m and vec V_r## are drawn.
2. We are to find out ##vecV_(mr)##, velocity of man with respect to rain. We know that ##vecV_(mr)=vecV_m-vecV_r## Therefore draw ##-vecV_r## at the tip of ##vecV_m##
3. Join the tail of ##vecV_m## to the tip of ##-vecV_r## to obtain ##vecV_(mr)## as velocity of man with respect to rain.