A particle is acted upon by constant forces `4hati+hatj-3hatk and 3hati+hatj-hatk` which displace it from a point `hati+2hatj+3hatk` to the point `5hati+4hatj+hatk`. The work done in standard units by the forces is given by

Options

A. 40 units
B. 30 units
C. 25 units
D. 15 units

Answer

A

Explanation

Total force, `F = (4hati + hatj - 3hatk) + (3hati + hatj - hatk)`
`F = 7hati + 2hatj - 4hatk`
The particle is displaced from
`A(hati + 2hatj + 3hatk) - (hati + 2hatj + 3hatk) = 4hati + 2hatj - 2hatk`
`:.` Work done `= F . AB=(7hati + 2hatj - 4hatk ). (4hati + 2hatj - 2hatk)`
`= 28 + 4 + 8 = 40` units