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

Options

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

Answer

C

Explanation

Given that , `v = 2 hati + hatj - hatk ` and w = ` hati + 3hatk`
Now , `v xx w = |{:( hati , hatj , hatk) , ( 2, 1 , -1) , (1 , 0 ,3 ):}|`
`= hati ( 3- 0 ) - hatj ( 6 + 1) + hatk ( 0- 1)`
`= 3hati - 7 hatj - hatk`
Now , `[uvw] = u * (v xx w)`
`= u * (3hati - 7 hatj - hatk)`
which is maximum , if angle between u and `3hat i - 7hatj - hatk ` is 0 and maximum value is `| 3hat i - 7 hatj - hatk| = sqrt(3^(2) + 7^(2) + 1^(2)) = sqrt(59)`