Show that the displacement vector does not depend upon the choece of the coordinate axes.

Explanation

Let a particle be displaced from location ` P to Q`, Fig. 2 (c ) .63. So the displacement vector,
` vec PQ) = vec r`.
.
Whith respect ot origion ` O`, let,
` vec (OP) =rr_(1) and vec (OQ) =_(2)`
With triangle law to origin `O'`. Let
` vec (O'P) =vec r'_(1) and vec (O'Q) = vec r'_(2)`
Using triangle law of vectors addition, we have
` vec _(1) + vec r=vec r or vec r =vec r_(2) -vec r_(1)`
Also, ` vec r+ vec r'_(1) =vec r'_(2) or vec r_(1) vec r'_(2) -vec r'_(1)`
so, `vec r =vec _(2) -vec r_(1) = vec r'_(2) -vecr'_(1)`
This show that the idsplacement vector ` vec r` is independent of the cjoice of origin.