If `veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk` and `vecc=hati+alphahatj+betahatk`
are linearly dependent vectors and `|vecc|=sqrt(3)` then

Options

A. `alpha=1, beta=-1`
B. `alpha=1, beta=+-1`
C. `alpha=-1,beta=+-1`
D. `alpha=+-1,beta=1`

Answer

D

Explanation

`veca, vecb, vecc` are linearly dependent vectors.
`:.[(veca, vecb, vecc)]=0`
`implies|(1,1,1),(4,3,4),(1,alpha, beta)|=0-beta+1=0=beta=1`
Also
`|vecc|=sqrt(3)`
`implies sqrt(1+alpha^(2)+beta^(2))=sqrt(3)`
`implies1+1+alpha^(2)=3impliesalpha^(2)=1impliesalpha=+-1`