Let `vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU` is a unit vector, then the maximum value of the scalar triple product `[ vecU vecV vecW]` is

Options

A. `-1`
B. `sqrt(10)+sqrt(6)`
C. `sqrt(59)`
D. `sqrt(60)`

Answer

C

Explanation

We have
`[(vecU, vecV, vecW)]=vecU.(vecVxxvecW)`
`implies[(vecU, vecV, vecW)]le|vecU||vecVxxvecW| [ :' veca. vecb le |veca||vecb|]`
`implies[(vecU, vecV, vecW)]le|vecVxxvecW| [ :' |vecU|=1]`
Now,
`vecVxxvecW=|(hati, hatj, hatk),(2,1,-1),(1,0,3)|=3hati-7hatj-hatk`
`:.|vecVxxvecW|=sqrt(9+49+1)=sqrt(59)`
Hence `[(vecU, vecV, vecW)]le sqrt(59)`