Question

7. ABCDEF is a regular hexagon, then find AB+AC+ AD+AE+AF. (O is the centre regular
hexagon)
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Answer 1

Answer:

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Answer 2

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:

1. DE = - AB
2. EF = - BC

• THESE TWO CONDITIONS ARE SATISFIED WHEN THE VECTORS ARE DISPLACED PARALLELLY.

• BECAUSE PARALLEL DISPLACEMENT DOESNOT AFFECT THE DIRECTION OF VECTORS.