Prove that the displacement vector does not depend upon the choice of the coordinate axes.
Answers
Answered by
2
Answer:
Let a particle be displaced from location
P→Q
P→Q
, Fig. 2 (c ) .63. So the displacement vector,
P
→
Q)=
r
→
P→Q)=r→
.
. Whith respect ot origion
O
O
, let,
OP
−
→
−
=r
r
1
and
OQ
−
→
−
=
2
OP→=rr1andOQ→=2
With triangle law to origin
O'
O′
. Let
O'P
−
→
−
=
r
→
'
1
and
O'Q
−
→
−
=
r
→
'
2
O′P→=r→′1andO′Q→=r→′2
Using triangle law of vectors addition, we have
–
→
(1)+
r
→
=
r
→
or
r
→
=
r
→
2
−
r
→
1
_→(1)+r→=r→orr→=r→2-r→1
Also,
r
→
+
r
→
'
1
=
r
→
'
2
or
r
→
1
r
→
'
2
−
r
→
'
1
r→+r→′1=r→′2orr→1r→′2-r→′1
so,
r
→
=
–
→
(2)−
r
→
1
=
r
→
'
2
−
r
→
'
1
r→=_→(2)-r→1=r→′2-r→′1
This show that the idsplacement vector
r
→
r→
is independent of the cjoice of origin.
Explanation:
Similar questions