Question

a particle is displaced from a position (2i-j+k) metre to another position (3i+2j-2k)metre under the action of force (2i+j-k)N.what will be the work done by the force​

Answer 1

$\huge{\underline{\underline{.........Answer.........}}}$

$\huge{\underline{Given:-}}$

${r_1 = 2 \hat{i} - \hat{j} + \hat{k}}$

${r_2 = 3 \hat{i} + 2 \hat{j} - 2 \hat{k}}$

${F = 2 \hat{i} + \hat{j} - \hat{k}}$

$\huge{\underline{Explanation:-}}$

For displacement

${S = r_2 - r_1}$

${S = 3 \hat{i} + 2 \hat{j} - 2 \hat{k} - 2 \hat{i} + \hat{j} - \hat{k}}$

${S = \hat{i} + 3 \hat{j} - 3 \hat{k}}$

Now, from work done formula

$\huge{\boxed{\boxed{W = F.S}}}$

${W = 2 \hat{i} + \hat{j} - \hat{k} \times \hat{i} + 3 \hat{j} - 3 \hat{k}}$

Scalar product should be taken

${W = 2 \times 1 + 1 \times 3 + -3 \times -3}$

${W = 2 + 3 + 9}$

${W = 14 units}$

$\huge{\boxed{\boxed{W = 14 units}}}$

so,work done by the force is 14 units.