Final answer:
The work done by a force can be calculated using the formula: Work = Force * distance * cos(theta). Apply this formula to the given values and calculate the work done by the force f=8i-6j+9k that moves an object from the point (0,10,8) to the point (6,12,20) along a straight line.
Step-by-step explanation:
The work done by a force is given by the formula:
Work = Force * distance * cos(theta)
where Force is the magnitude of the force, distance is the displacement, and theta is the angle between the force and displacement vectors.
In this case, the force F = 8i - 6j + 9k, and the displacement is from the point (0,10,8) to the point (6,12,20).
The distance can be calculated using the distance formula: distance = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
Plugging in the values, we get a distance of sqrt((6-0)^2 + (12-10)^2 + (20-8)^2) = sqrt(36 + 4 + 144) = sqrt(184).
Using the formula for work, we have:
Work = (8i - 6j + 9k) * sqrt(184) * cos(theta)
Since the displacement is along a straight line, the angle between the force and displacement vectors is 0 degrees, so:
Work = (8i - 6j + 9k) * sqrt(184) * cos(0)
Work = (8i - 6j + 9k) * sqrt(184)
Work = 8 * sqrt(184)i - 6 * sqrt(184)j + 9 * sqrt(184)k