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The work done by the force $\overrightarrow {f}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ acting on a particle, if the particle is displaced from $A(3 , 3 , 3 )$ to the point $B(4 , 4 , 4 ) $ is

\[\begin{array}{1 1}(1) 2 units &(2)3 units\\(3) 4 units &(4) 7 units\end {array}\]

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${F}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$
$\overrightarrow {d}=(4\overrightarrow{i}+4\overrightarrow{j}+4\overrightarrow{k})-(3\overrightarrow{i}+3\overrightarrow{j}+3\overrightarrow{k})$
$\overrightarrow{d}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$
Work done =$ \overrightarrow{F} . \overrightarrow {d}$
$\qquad=(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}).(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k})$
$\qquad= 1 \times - 1 \times 1 -1 \times 1 =3 units$
Hence 2 is the correct answer.
answered May 13, 2014 by meena.p
 

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