7. ABCDEF is a regular hexagon, then find AB+AC+ AD+AE+AF. (O is the centre regular
hexagon)
Answers
Answer:
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ANSWER:
AB + AC + AD + AE + AF = 6 AO
GIVEN:
ABCDEF IS REGULAR HEXAGON WITH O AS CENTRE.
TO FIND:
AB + AC + AD + AE + AF
EXPLANATION:
AB = AB
ACCORDING TO TRIANGLE LAW OF VECTORS
AC = AB + BC
AD = AC + CD
AD = AB + BC + CD
AE = AD + DE
AE = AB + BC + CD + DE
AF = AE + EF
AF = AB + BC + CD + DE + EF
AB + AC + AD + AE + AF = AB + AB + BC + AB + BC + CD + AB + BC + CD + DE + AB + BC + CD + DE + EF
AB + AC + AD + AE + AF = 5 AB + 4 BC + 3 CD + 2 DE + EF
DE = - AB
EF = - BC
AB + AC + AD + AE + AF = 5 AB + 4 BC + 3 CD - 2 AB - BC
AB + AC + AD + AE + AF = 3 AB + 3 BC + 3 CD
AB + AC + AD + AE + AF = 3 (AB + BC + CD)
AB + AC + AD + AE + AF = 3 AD
GIVEN HEXAGON IS REGULAR HEXAGON AO = BO = CO = DO = EO = FO
AD = AO + DO
AD = 2 AO
AB + AC + AD + AE + AF = 3(2 AO )
AB + AC + AD + AE + AF = 6 AO
NOTE 1: TAKE BOLD LETTERS AS VECTORS.
NOTE 2: DIAGRAMS IN ATTACHMENT.
EXTRA POINTS:
- DE = - AB
- EF = - BC
- THESE TWO CONDITIONS ARE SATISFIED WHEN THE VECTORS ARE DISPLACED PARALLELLY.
- BECAUSE PARALLEL DISPLACEMENT DOESNOT AFFECT THE DIRECTION OF VECTORS.
