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Work Done as Dot Product

Three forces ...

Question

Three forces $3 (^i + 3^j +^k), \frac{5}{7} (- 2^i + 9^k)$ and $11 (2^i +^j + 6^k)$ are acting on a particle. Calculate the work done in displacing the particle from point $(4, - 1, 1)$ to point $(11, 6, 8)$ .

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Solution

Net force $F = 3 (i + 3 j + k) + \frac{5}{7} (- 2 i + 9 k) + 11 (2 i + j + 6 k)$

$⟹ F = \frac{165}{7} i + 20 j + \frac{528}{7} k$

$\to r = (11 i + 6 j + 8 k) - (4 i - j + k) = 7 i + 7 j + 7 k$

Work done $W = \to F . \to r = 165 + 140 + 528$

$⟹ W = 833 J$

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