A constant force $\overrightarrow{\mathbf{F}} = 2\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}}$ is acting on a particle such that the particle is displaced from the point(1,2,3) to the point (3,4,5). The work done by the force is

Question

Dr. Abubacker · Accepted Answer

(a)
Let $\overrightarrow{\mathbf{OA}} = \widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + 3\widehat{\mathbf{k}}$ and $\overrightarrow{\mathbf{OB}} = 3\widehat{\dot{\mathbf{i}}} + 4\widehat{\dot{\mathbf{j}}} + 5\widehat{\mathbf{k}}$
$	herefore\ \overrightarrow{\mathbf{AB}} = 2\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}}$
$	herefore$ work don, $W = \overrightarrow{\mathbf{F}} \bullet \overrightarrow{\mathbf{AB}}$
$= \left( 2\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}} ight) \bullet \left( 2\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}} ight)$
$= 4 - 6 + 4 = 2$

Q. A constant force $\overrightarrow{\mathbf{F}} = 2\widehat{\dot{\mathbf{i}}} - 3\widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}}$ is acting on a particle such that the particle is displaced from the point(1,2,3) to the point (3,4,5). The work done by the force is

Explanation

Reviewed by Dr. Abubacker

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