# A force 6i+3j+k displaces an object from A(0,3,2) to B(5,1,6) what is the work done?

Aug 9, 2018

The work done is $= 28 J$

#### Explanation:

The work is the dot product of force and distance

The force is

$\vec{F} = < 6 , 3 , 1 >$

The displacement is

$\vec{A B} = < 5 - 0 , 1 - 3 , 6 - 2 > = < 5 , - 2 , 4 >$

The work is

$W = \vec{F} . \vec{A B} = < 6 , 3 , 1 > . < 5 , - 2 , 4 >$

$= \left(6 \times 5\right) + \left(3 \times - 2\right) + \left(1 \times 4\right)$

$= 30 - 6 + 4$

$= 28 J$