Respuesta :
Answer:
102 J
Explanation:
Work done by a force
= Force x displacement
In case of vector form of force and displacement , we take dot product of force and displacement to calculate work.
The vector form of line which joins the two given points is given by the equation
d = (4-0) i +(16 - 10)j +( 18 - 4 )k
= 4i +6j +14k
Work done = F . d
(6 i -8J+9k) . ( 4i +6 j + 14 k )
24-48 +126
= 102 J
Answer:
102 J
Explanation:
Given that, the force of a moving object is,
[tex]F = (6i-8j + 9k) N[/tex]
The object is moving from point (0,10,4) to the point (4,16,18).
Now we can calculate the displacement by the formula,
[tex]dr=(x_{2}- x_{2})i+(y_{2}- y_{2})j+(z_{2}- z_{2})k[/tex]
Put all the values from the given values.
[tex]dr=(4- 0)i+(16-10)j+(18-4)k\\dr=(4i+6j+14k) meters[/tex]
Now, the work done can be calculated as,
[tex]W=F.dr[/tex]
Therefore,
[tex]W=(6i-8j + 9k).(4i+6j+14k)\\W=102J[/tex]
Therefore, work done is 102 J
