If the magnitude of the moment about the pont `hatj+hatk` of a force `hati+alphahatj-hatk` acting through the point `hati+hatj` is`sqrt(8)`, then the value of `alpha` is

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

B

Explanation

Let `vecM` be the moment of the force `vecF=hati+alphahatj-hatk`
acting through the point `A(hati+hatj)` about the point `O(hatj+hatj)`.
Then
`vecM=vec(OA)xxvecF`
`impliesvecM=(hati-hatk)xx(hati+alpha hatj-hatk)`
`=vecM=|(hati, hatj, hatk),(1,0,-1),(1,alpha,-1)|=alpha hati+alphahatk`
`implies|vecM|=sqrt(alpha^(2)+alpha^(2))=sqrt(2)|alpha|`
`implies sqrt(2)|alpha|=sqrt(2) [ :' |vecM|=sqrt(8) "(given)" ]`
`implies|alpha|=2impliesalpha=-2`