A particle acted upon by constant forces $4\widehat{\mathbf{i}} + \widehat{\mathbf{j}} - 3\widehat{\mathbf{j}}$ and $3\widehat{\mathbf{i}}\mathbf{+}\widehat{\mathbf{j}}\mathbf{-}\widehat{\mathbf{k}}$is displaced from the point $\widehat{\mathbf{i}} + 2\widehat{\mathbf{j}}\mathbf{+}3\widehat{\mathbf{k}}$ to the point $5\widehat{\mathbf{i}}\mathbf{+ 4}\widehat{\mathbf{j}}\mathbf{+}\widehat{\mathbf{k}}$ .The total work done by the forces in SI unit is

Question

Dr. Abubacker · Accepted Answer

(b) Work done,$W = F \bullet ds = \left( F_{1} + F_{2} \right) \bullet \left( s_{2} - s_{1} \right)$
=$\left\{ (4\widehat{i} + \ \widehat{j} - 3\widehat{k)} + \left( 3\widehat{i} + \widehat{j} - \widehat{k} \right) \right\}$
$\left\{ \left( 5\widehat{i} + 4\widehat{j} + \widehat{k} \right) - \left( \widehat{i} + 2\widehat{j} + 3\widehat{k} \right) \right\}\ $
$= \left( 7\widehat{i} + 2\widehat{j} - 4\widehat{k} \right).\left( 4\widehat{i} + 2\widehat{j} - 2\widehat{k} \right)$
$= 28 + 4 + 8 = 40\ J$

Explanation

Reviewed by Dr. Abubacker

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