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Question: A force \(6\widehat{i} + 3\widehat{j} + \widehat{k}\) Newton displaces a particle from A(0, 3, 2) to...

A force 6i^+3j^+k^6\widehat{i} + 3\widehat{j} + \widehat{k} Newton displaces a particle from A(0, 3, 2) to B(5, 1, 6). Find the work done.

A

10 J

B

22 J

C

28 J

D

41 J

Answer

28 J

Explanation

Solution

d→=5i^−2j^+4k^\overrightarrow{d} = 5\widehat{i} - 2\widehat{j} + 4\widehat{k}

W = F→.d→=(6i^+3j^+k^).(5i^−2j^+4k^)=28J\overrightarrow{F}.\overrightarrow{d} = \left( 6\widehat{i} + 3\widehat{j} + \widehat{k} \right).\left( 5\widehat{i} - 2\widehat{j} + 4\widehat{k} \right) = 28J