Constant forces ${\overrightarrow{\mathbf{P}}}_{1} = \widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}\$, ${\overrightarrow{\mathbf{P}}}_{2} = - \widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}}$ and ${\overrightarrow{\mathbf{P}}}_{3} = \widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}}$ act on a particle at point $A$. The work done when the particle is displaced from the point $A$ to $B$ where ${\overrightarrow{\mathbf{A}}}_{\ } = 4\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} - 2\widehat{\mathbf{k}}$ and ${\overrightarrow{\mathbf{B}}}_{\ } = 6\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}}$ is

Question

Dr. Abubacker · Accepted Answer

(d)
$	herefore$ Total force $\overrightarrow{\mathbf{P}} = {\overrightarrow{\mathbf{P}}}_{1} + {\overrightarrow{\mathbf{P}}}_{2} + {\overrightarrow{\mathbf{P}}}_{3}$
$= \widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}} - \widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}} + \widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}} = 2\widehat{\dot{\mathbf{j}}}$
and displacement $\overrightarrow{\mathbf{AB}} = 6\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}} - \left( 4\widehat{\dot{\mathbf{i}}} + 3\widehat{\dot{\mathbf{j}}} - 2\widehat{\mathbf{k}} ight)$
$= 2\widehat{\dot{\mathbf{i}}} + 4\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}}$
$	herefore$Work done $= \overrightarrow{\mathbf{P}} \bullet \overrightarrow{\mathbf{AB}}$
$= 2\widehat{\dot{\mathbf{j}}}\left( 2\widehat{\dot{\mathbf{i}}} + 4\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}} ight) = 8$

Explanation

Reviewed by Dr. Abubacker

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