The radius vector and linear momentum are respectively given by vectors `2hati + hatj + hatk` and `2hati - 3hatj + 3hatk` Then the angular momentum is

Options

A. `2hati - 4hatk`
B. `4 hati- 8 hatk`
C. `2hati - 4 hatj +2hatk`
D. `4 hati - 8 hatj`

Answer

B

Explanation

Given radius vector , `vecr = 2 hati + hatj + hatk`
Linear momentum `, vecp = 2 hati - 3hatj + hatk`
As angular momentum , `vecL = vecr xx vecp = |{:(hati , hatj , hatk) , (2 , 1 , 1) , (2 , -3 , 1):}|`
`= hati (1 - (-3)) - hatj (2 - 2) + hatk (-6 - 2) = 4 hati - 8 hatk`