Given below in Column-I are the relations between vectors \(a,\) \(b,\) and \(c\) and in Column-II are the orientations of \(a,\) \(b,\) and \(c\) in the XY-plane. Match the relation in Column-I to the correct orientations in Column-II.
 

Column-I Column-II
a \(a + b = c\) (i)
b \(a- c = b\) (ii)
c \(b - a = c\) (iii)
d \(a + b + c = 0\) (iv)

1. a(ii), b (iv), c(iii), d(i)
2. a(i), b (iii), c(iv), d(ii)
3. a(iv), b (iii), c(i), d(ii)
4. a(iii), b (iv), c(i), d(ii)

 
Hint: Apply triangle law of vector addition.
Step 1: Consider the adjacent diagram in which vectors A and B are corrected by head and tail.

Resultant vector C = A + B
(a) from (iv) it is clear that c = a + b
(b) from (iii) c + b = a  a - c = b
(c) from (i) b = a +c  b - a = c
(d) from (ii) - c = a + b  a + b + c = 0