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In a Pentagon PQRS prove that vectorbPT+QR+SR+TS+PR=3PR

In a Pentagon PQRS prove that vectorbPT+QR+SR+TS+PR=3PR

Grade:12

1 Answers

Arun
25750 Points
6 years ago
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→= RHS
Hence proved.

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