Prove that PQ + QR + RS + SP = 0 in the given quadrilateral
PQRS​

Step-by-step explanation:

Using ∆ law of vector addition,

PR→=PQ→+QR→PR→=PQ→+QR→ - (i)

Also,

RP→=RS→+SP→RP→=RS→+SP→ - (ii)

Taking LHS,

=PQ→+QR→+RS→+SP→=PQ→+QR→+RS→+SP→

[Put value of PR→=PQ→+QR→PR→=PQ→+QR→ from equation (i) ]

=(PR→)+RS→+SP→=(PR→)+RS→+SP→

[Put value of RP→=RS→+SP→RP→=RS→+SP→ from equation (ii) ]

=PR→+RP→=PR→+RP→

=PR→−PR→=PR→−PR→

=0=0

RHS