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If ABCDEF is a regular hexagon with vec(...

If `ABCDEF` is a regular hexagon with `vec(AB) = veca` and `vec(BC)= vecb,` then `vec(CE)` equals

A

b - a

B

`- b`

C

b - 2a

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
In `DeltaABC, AB + BC = AC`
implies AC = a + b
AD is parallel to BC and AD = 2BC

`therefore AD = 2b`
In `DeltaACD`, AC + CD = AD
`implies CD=2b-(a+b)=b-a`
Now, `CE = CD + DE = (b-a)-a=b-2a`
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