If ` vec a ,\ vec b` are the vectors forming consecutive sides of a regular of a regular hexagon `A B C D E F ,\ ` then the vecrtor representing side `C D` is ` vec a+ vec b` b. ` vec a- vec b` c. ` vec b- vec a` d. `-( vec a+ vec b)`

Options

A. `vec a + vec b `
B. ` vec a - vec b `
C. `vec b - vec a `
D. `-(veca +vec b)`

Answer

C

Explanation

Using vector addition in `Delta ABC,` we have
`vec(AB) + vec(BC) = vec(AC) rArr veca + vec b = vec (AC)`

Clearly, AD is parallel to BC and AD = 2BC
`therefore vec(AD)=2 vec(b)`
In ` Delta ACD,` we have
`vec(AC)+vec(CD)=vec(AD) rArr veca + vecb + vec(CD) = 2 vecb rArr vec(CD)=vecb-veca`