Let ` vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot` If ` vec U` is a unit vector, then the maximum value of the scalar triple product `[UVW]` is a.`-1` b. `sqrt(10)+sqrt(6)` c. `sqrt(59)` d. `sqrt(60)`

Options

A. `-1`
B. `sqrt10 + sqrt6`
C. `sqrt59`
D. `sqrt60`

Answer

c

Explanation

Given that `vecV = 2hati +hatj -hatk and vecW =hati + 3hatk and vecU` is a unit vector
` |vecU|=1`
Now `|vecU vecV vecW] = vecU.(vecV xx vecW)`
`= vecU . (2hati +hatj -hatk) xx ( hati + 3hatk)`
`vecU . (3hati -7hatj - hatk)`
` sqrt(3^(2)+7^(2)+ 1^(2)) cos theta`
Which is maximum when `cos theta =1`
therefore, maximum value of [`vecU vecV vecW] - sqrt59`