Answer:
The work done by a constant force F = -1i + 4j -5k moving an object along a straight line from point -6,-8,7 to point -7,-10,1) can be calculated using the formula:
Work = ∫F·dr
where F is the force vector and dr is the displacement vector.
In this case, we can use the given force vector F = -1i + 4j -5k and the displacement vector dr = (7 - 6, 10 - 8, 1 - 7) meters.
Substituting these values into the formula, we get:
Work = ∫(-1i + 4j -5k)·(7 - 6, 10 - 8, 1 - 7)
Work = ∫(-1, 4, -5)·(7 - 6, 10 - 8, 1 - 7)
Work = ∫(-1, 4, -5)·(1, 2, -1)
Work = 1 - 4 - 5 = -8
So, the work done by the force F = -1i + 4j -5k moving the object from point -6,-8,7 to point -7,-10,1) is -8 Joules.
Answer: -8 Joules
Explanation: