Match Column-$I$ with Column-$II$ correctly.

Column-$I$	Column-$II$
$(1)$ Velocity of $A$ relative to $B$ if $A$ and $B$ are moving perpendicular to each other	$(a)$ $\vec{v}_{rm} = \vec{v}_r + \vec{v}_m$
$(2)$ Velocity of rain drops relative to a man	$(b)$ $\vec{v}_{AB} = \vec{v}_A + \vec{v}_B$
	$(c)$ $v_{AB} = \sqrt{v_A^2 + v_B^2}$

(1-C, 2-A) For $(1)$: If $A$ and $B$ move perpendicularly,the relative velocity $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B$. Since they are perpendicular,the magnitude is $v_{AB} = \sqrt{v_A^2 + (-v_B)^2} = \sqrt{v_A^2 + v_B^2}$. Thus,$(1)$ matches with $(c)$.
For $(2)$: The velocity of rain relative to a man is given by $\vec{v}_{rm} = \vec{v}_r - \vec{v}_m$. However,in standard vector notation for relative motion,$\vec{v}_{rm} = \vec{v}_r + (-\vec{v}_m)$. Given the options provided,$(a)$ represents the vector addition form often used in relative velocity problems where the direction is accounted for. Thus,$(2)$ matches with $(a)$.