Given `|veca|=|vecb|=1 and |veca + vecb|= sqrt3` if `vecc` is a vector such that `vecc -veca - 2vecb = 3(veca xx vecb) ` then find the value of `vecc . vecb`.

Options

A. `-1/2`
B. `1/2`
C. `3/2`
D. `5/2`

Answer

D

Explanation

We have
`|veca+vecb|=sqrt(3)`
`implies|veca+vecb|^(2)=3`
`implies|veca|^(2)+|vecb|^(2)+2(veca.vecb)=3`
`implies1+1+2(veca.vecb)=3impliesveca.vecb=1/2`…………….i
Now
`vecc-veca-2vecb=3(vecaxxvecb)`
`implies(vecc-veca-2vecb).vecb=3{(vecaxxvecb).vecb}`
`impliesvecc.vecb-veca.vecb-2(vecb.vecb)=0 [ :' [(veca, vecb, vecb)]=0]`
`impliesvecc.vecb-1/2-2xx1=0` [Using i ]
`impliesvecc.vecb=5/2`