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Constant forces $\bar{P} = 2 \bar{i} - 5 \bar{j} + 6 \bar{k} and \bar{Q} = - \bar{i} + 2 \bar{j} - \bar{k}$ act on a particle, determine the work done when the particle is displaced from the point A with position vector $4 \bar{i} - 3 \bar{j} - 2 \bar{k}$ to a point B with position vector $6 \bar{i} + \bar{j} - 3 \bar{k}$

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answer is -15.

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Detailed Solution

$W = \bar{F} \cdot \bar{s}, \bar{F} = \bar{P} + \bar{Q}, \bar{S} = \bar{A B};$

$\bar{F} = \bar{i} - 3 \bar{j} + 5 \bar{k}; \bar{S} = \bar{A B} = \bar{O B} - \bar{O A}$

$= 2 \bar{i} + 4 \bar{j} - \bar{k} \Rightarrow \bar{F} \cdot \bar{S} = - 15$

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