# A particle is acted upon by constant forces $\dpi{100} 4\hat{i}+\hat{j}-3\hat{k}\; and\; 3\hat{i}+\hat{j}-\hat{k}\;$ which displace it from a point $\dpi{100} \hat{i}+2\hat{j}+3\hat{k}\;$ to the point $\dpi{100} 5\hat{i}+4\hat{j}+\hat{k}\;$ . The work done in standard units by the forces is given by Option 1) 25 Option 2) 30 Option 3) 40 Option 4) 15

As we learnt in

Applications of Vectors -

$\vec{W}= \vec{F}.\vec{S}$

- wherein

Work done against a constant force $\vec{F}$ over a displacement $\vec{S}$

Work done by forces $\vec{F_1}\: and \:\vec{F_2}\:is$

$(\vec{F_1}\: + \:\vec{F_2}).\vec{d}$

$\vec{F_1}\: + \:\vec{F_2}=(4\hat{i}+\hat{j}-3\hat{k}) + (3\hat{i}+\hat{j}-\hat{k})$

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

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

$\vec{d}= (4\hat{i}+\hat{2j}-\hat{2k})$

Work done = $=(\vec{F_1}+\vec{F_2}).\vec{d}$

$= (7\hat{i}+\hat{2j}-\hat{4k}).(4\hat{i}+\hat{2j}-\hat{2k})$

$= 28+4+8 =40$

Option 1)

25

Incorrect

Option 2)

30

Incorrect

Option 3)

40

Correct

Option 4)

15

Incorrect

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