a) `vec(PQ)-vec(RQ)+vec(RS)=vec(PQ)+vec(QR)+vec(RS)`

using Chasles relation

`vec(PQ)+vec(QR)=vec(PR)`

Therefore

`vec(PQ)-vec(RQ)+vec(RS)=vec(PR)+vec(RS)`

Using Chasles relation again

**Answer:** `vec(PQ)-vec(RQ)+vec(RS)=vec(PS)`

b) `vec(PS)+vec(RQ)-vec(RS)-vec(PQ)=vec(PS)+vec(RQ)+vec(SR)+vec(QP)`

`vec(PS)+vec(RQ)-vec(RS)-vec(PQ)=(vec(PS)+vec(SR))+(vec(RQ)+vec(QP))`

`vec(PS)+vec(RQ)-vec(RS)-vec(PQ)=vec(PR)+vec(RP)=vec(PP)=vec0`

**Answer:** `vec(PS)+vec(RQ)-vec(RS)-vec(PQ)=vec(0)`

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a) `vec(PQ)-vec(RQ)+vec(RS)=vec(PQ)+vec(QR)+vec(RS)`

using Chasles relation

`vec(PQ)+vec(QR)=vec(PR)`

Therefore

`vec(PQ)-vec(RQ)+vec(RS)=vec(PR)+vec(RS)`

Using Chasles relation again

**Answer:** `vec(PQ)-vec(RQ)+vec(RS)=vec(PS)`

b) `vec(PS)+vec(RQ)-vec(RS)-vec(PQ)=vec(PS)+vec(RQ)+vec(SR)+vec(QP)`

`vec(PS)+vec(RQ)-vec(RS)-vec(PQ)=(vec(PS)+vec(SR))+(vec(RQ)+vec(QP))`

`vec(PS)+vec(RQ)-vec(RS)-vec(PQ)=vec(PR)+vec(RP)=vec(PP)=vec0`

**Answer:** `vec(PS)+vec(RQ)-vec(RS)-vec(PQ)=vec(0)`