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# An object is displaced from point $A(2m,3m,4m)$ to a point B $(1m, 2m, 3m)$ under a constant force. $\hat F=(2 \hat i+3 \hat j+4 \hat k)$. Find the work done by the force

$(a)\;-9\;J \quad (b)\;6 \;J \quad (c)\; 9 \;J \quad (d)\;-6\;J$

$W=\hat F.\hat {ds}$
$\hat {ds}=\hat r_f-\hat r_i$
$\hat {ds}=(\hat i+2 \hat j+3 \hat k)-(2 \hat i+3 \hat j+4 \hat k)$
$\quad=(-\hat i-\hat j-\hat k)$
$W=(2 \hat i+3 \hat j+4 \hat k).(-\hat i - \hat j -\hat k)$
$\quad= -9 J$
Hence a is the correct answer.

edited Feb 17, 2014 by meena.p