A particle has the position vector `r = hati - 2 hatj + hatk` and the linear momentum `p = 2 hati - hatj + hatk.` . Its angular momentum about the origin is

Options

A. `- hati + hatj - 3 hatk `
B. `- hati + hatj + 3 hatk`
C. `hati - hatj + 3 hatk`
D. `hati - hatj - 5 hatk`

Answer

B

Explanation

Given,
`r = hati - 2 hatj + hatk`
`p = 2 hati - hatj + batk`
Anglular momentum
`J = r xx p`
`= (hati - 2 hatj + hatk) xx ( 2 hati - hatj + hatk)`
`J = [{:(hati, hatj , hatk), ( 1, -2,1),(2, -1, 1):}|`
`J = hati ( -2 +1) - hatj ( 1-2) + hatk(-1 + 4)`
`hatj =- hati + hatj + 3 hatk`