Discussion Forum

A force  (F)=$-5\hat{i}-7\hat{j}+3\hat{k}$ acting on a partcle  causes a dispalcement (s)=  $3\hat{i}-2\hat{j}+a\hat{k}$  in its own direction. If the work done  is 14J , then  the value of 'a' is 

Answer:

Explanation:

 GIven,   F=$-5\hat{i}-7\hat{j}+3\hat{k}$.

  s=  $3\hat{i}-2\hat{j}+a\hat{k}$

 and W=14 J

 the work done by a force in displaceing a particle  through  a distance is given by 

 W= F.s ........(i)

 Substituting above values in Eq.(i), we get

$14=  (-5\hat{i}-7\hat{j}+3\hat{k}).( 3\hat{i}-2\hat{j}+a\hat{k})$

 $\Rightarrow$    $ 14=  -15+14+3a$

$\Rightarrow $    $ a=\frac{15}{3}=5$