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In a Pentagon PQRS prove that vectorbPT+QR+SR+TS+PR=3PR
LHS = PQ→ + PT→ + QR→ + SR→ + TS→ + PR→= PQ→ + QR→ + PT→ + TS→ + SR→ + PR→= PR→ +PS→ + SR→ + PR→ [∵ PQ→ + QR→ = PR→ and PT→ + TS→ = PS→]= PR→ + PS→ + PR→ – PS→ + PR→ [∵ PS→ + SR→= PR→ ⇒ SR→ = PR→ – PS→ ]= 3 PR→= RHSHence proved.
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