F⃗=(−2i^+3j^+4k^)N \vec{F} = \left ( - 2 \hat{i} + 3 \hat{j} + 4 \hat{k} \right ) N force applied on a particle and the particle moves fromm (3,-4,-2) to (-2,3,5). What is the amount of work done?

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Accepted Answer

খ. 59 J

ব্যাখ্যা: কণার সরণ $\Delta \vec{r} = \vec{r}_2 - \vec{r}_1 = (-2 - 3)\hat{i} + (3 - (-4))\hat{j} + (5 - (-2))\hat{k} = -5\hat{i} + 7\hat{j} + 7\hat{k}$। কৃতকাজ $W = \vec{F} \cdot \Delta \vec{r} = (-2\hat{i} + 3\hat{j} + 4\hat{k}) \cdot (-5\hat{i} + 7\hat{j} + 7\hat{k}) = (-2)(-5) + (3)(7) + (4)(7) = 10 + 21 + 28 = 59	ext{ J}$।

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