If `|vecAxxvecB|=sqrt(3) vecA.vecB`, then the value of `|vecA+vecB|` is

Options

A. `(A^(2)+B^(2)+(AB)/(sqrt3))^(1/(2))`
B. `A+B`
C. `(A^(2)+B^(@)+sqrt3AB)^(1/(2))`
D. `(A^(2)+B^(2)+AB)^(1/(2))`

Answer

D

Explanation

(d): `|vecAxxvecB|=sqrt3vecA.vecB`
`A B sin theta =sqrt3 A B cos theta`
`tan theta=sqrt3`
`rArr theta=(pi)/(3)`
`cos theta =cos ((pi)/(3))=(1)/(2)`
`|vecA+vecB|^(2)=|vecA|^(2)+|vecB|^(2)+2vecA.vecB`
`=A^(2)+B^(2)+2AB cos theta`
`=A^(2)+B^(2)+AB`
`vecA+vecB=(A^(2)+B^(2)+AB)^(1/(2))`