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Question 212

A particle is acted upon by constant forces $$4\hat{i} + \hat{j} - 3\hat{k}$$ and $$3\hat{i} + \hat{j} - \hat{k}$$ which displace it from a point $$\hat{i} + 2\hat{j} + 3\hat{k}$$ to the point $$5\hat{i} + 4\hat{j} + \hat{k}$$. The work done in standard units by the forces is given by

Solution

The resultant force is

$$\vec F=(4\hat i+\hat j-3\hat k)+(3\hat i+\hat j-\hat k)$$

$$=7\hat i+2\hat j-4\hat k$$

The displacement vector is

$$\vec s=(5\hat i+4\hat j+\hat k)-(\hat i+2\hat j+3\hat k)$$

$$=4\hat i+2\hat j-2\hat k$$

The work done is

$$W=\vec F\cdot\vec s$$

$$=(7\hat i+2\hat j-4\hat k)\cdot(4\hat i+2\hat j-2\hat k)$$

$$=28+4+8$$

$$=40$$

Hence,

$$\boxed{40}$$

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