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A force $\vec{F} = (4 \hat{i} - 3 \hat{j} - 7 \hat{k}) N$ displaces a particle from point P(0,1,4) to point Q(2,3,2).Then the work done by the force is

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16 N

14 N

12 N

10 N

answer is A.

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Detailed Solution

$\vec{F} = 4 i - 3 j - 7 k$

${\vec{r}}_{1} = j + 4 k {\vec{r}}_{2} = 2 i + 3 j + 2 k$

$\vec{s} = {\vec{r}}_{2} - {\vec{r}}_{1} = 2 i + 2 j - 2 k$

$w = \vec{F} . \vec{s} = 8 - 6 + 14 = 16 N$

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