Find the work done by a force f = 6i − 8j + 9k that moves an object from the point (0, 10, 4) to the point (4, 16, 18) along a straight line. the distance is measured in meters and the force in newtons.

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

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.