A paticle acted on by constant forces 4h...

A paticle acted on by constant forces `4hati=hatj-3hatk and 3hati+hatj-hatk` is displaced from the point `hati+2hatj+3hatk to 5hati+4hatj+hatk`. Find the work done

40 units

30 units

25 units

15 units

Text Solution

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The correct Answer is:

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

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