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A particle moves from position vec(r1) =...

A particle moves from position `vec(r_1) = (2hati + 3hatj)m` to `vec(r_2) = (3hati + 7hatj)m` under the action of a force `F = (10hati +13hatj) N`.Calculate work done.

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We are given `vecF = (10hati + 13hatj) N implies vec(r_1) = (2hati + 3hatj)m`
`vec(r_2) = (3hati + 7hatj)m implies dvecr = vec(r_2) - vec(r_1) = [(3hati + 7hatj) - (2hati + 3hatj)]m`
`dvecr = (hati + 4hatj)m`
Work done `(W) = vecF .dvecr = (10 hati + 13 hatj) .(hati + 4hatj) = 10 + 52`
Work done by force `(vecF) = 62 J`
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