`ABCDEF` is a regular hexagon, Fig. 2 (c ) .65. What is the value of
` (vec (AB) + vec (AC) + vec (AD) + vec (AE) + vec (AF) ?`
.

Options

A. `vec(AO)`
B. `2 vec(AO)`
C. `4 vec(AO)`
D. `6 vec(AO)`

Answer

D

Explanation

`vec(AB) + vec(AC) + vec(AD) + vec(AE) + vec(AF)`
`= vec(AB) + (vec(AB) + vec(BC) + vec(CD))`
` + (vec(AB) + vec(BC) + vec(CD) + vec(DE))`
` + (vec(AB) + vec(BC) + vec(CD) + vec(DE) + vec(EF))`
`vec(AB) = - vec(DE) , vec(EC) = - vec(EF)`
`= 3(vec(AB) + vec(BC) + vec(CD)) = 3 (vec(AD)) = 6 vec(AO)`