# How is the resultant displacement affected when two displacement vectors are added in a different order?

*print*Print*list*Cite

### 1 Answer

You need to remember that the resulting vector `barr` is not influenced by the order of addition of two vectors `bar (v_1)` and `bar(v_2).`

`bar (v_1) +bar(v_2) = bar (v_2)+ bar(v_1) = bar r`

You may use analytical method to prove the independence of resulting vector of order of addition such that:

`bar (v_1) = v_(1x) bar i + v_(1y) bar j`

`bar (v_2) = v_(2x) bar i + v_(2y) bar j`

`bar r = r_x bar i + r_y bar j`

`bar (v_1) +bar(v_2) = v_(1x) bar i + v_(1y) bar j+v_(2x) bar i + v_(2y) bar j`

`bar (v_1) +bar(v_2) = (v_(1x)+v_(2x)) bar i + (v_(1y)+v_(2y)) bar j`

Substituting `r_x` for `(v_(1x)+v_(2x))` and `r_y` for`(v_(1y)+v_(2y))` yields:

`bar (v_1) +bar(v_2) =r_x bar i +r_y bar j`

**Hence, by commutative law of addition, the resultant displacement vector is the same, regardless the order of addition of the vectors**.