ABCDEF is a regular hexagon. Find the vector `vec AB + vec AC + vec AD + vec AE + vec AF` in terms of the vector `vec AD`

Options

A. 1
B. 2
C. 3
D. none of these

Answer

C

Explanation

`vec(AB) + vec(AC) + vec(AD) + vec(AE)+vec(AF)`
`=vec(ED) + vec(AC) + vec(AD) + vec(AE) + vec(CD) [therefore vec(AB) = vecED, vecAF= vecCD]`
`vec(AC)+vec(CD)+(vec(AE)+vec(ED))+vec(AD)`
`=vec(AD)+vec(AD) +vec(AD) = 3vec(AD)`