• # question_answer 4) A force $\vec{F}=3\hat{i}+c\hat{j}+2\hat{k}$ acting on a particle cause a displacement $\vec{S}=-4\hat{i}+2\hat{j}+3\hat{k}$ in its own direction. If the work done is 6J, then the value of c will be: A)  12                  B)  6C)  1                    D)  0

Given,     Force    $\vec{F}=3\hat{i}+c\hat{j}+2\hat{k}$ Displacement     $\vec{S}=-\,4\hat{i}+2\hat{j}+3\hat{k}$ Work done                   $W=6\,J$ and workdone is given by             $W=\vec{F}\times S$ $\Rightarrow$               $6=\left( 3\hat{i}+c\hat{j}+2\hat{k} \right)\,.\,\left( 4\hat{i}+2\hat{j}+3\hat{k} \right)$ $\Rightarrow$               $6=-12+2c+6$ $\Rightarrow$               $6=-6+2c$ $\Rightarrow$               $2c=12$ $\Rightarrow$               $c=6$