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  4. A particle moves from position 3 hati+2 hatj-6 hatk to 14 hati+13 hatj+9 hatk due to a uniform force of (4 hati+ hatj+3 hatk) N. If the displacement. In metre then work done will be

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Q. A particle moves from position $3 \hat{i}+2 \hat{j}-6 \hat{k}$ to $14 \hat{i}+13 \hat{j}+9 \hat{k}$ due to a uniform force of $(4 \hat{i}+\hat{j}+3 \hat{k}) N$. If the displacement. In metre then work done will be

Work, Energy and Power

Solution:

$S=\vec{r}_2-\vec{r}_1=(14 \hat{i}+13 \hat{j}+9 \hat{k})-(3 \hat{i}+2 \hat{j}-6 \hat{k})$
$W=\vec{F} \cdot \vec{S}=(4 \hat{i}+\hat{j}+3 \hat{k}) \cdot(11 \hat{i}+11 \hat{j}+15 \hat{k})$
$=4 \times 11+1 \times 11+3 \times 15=100\, J$