Find the total work done by a 15 N force F in the direction of x=(1,2,2), when it moves a particle from O to P(1,-3,4), and then from P to A(7,2,5).

The distance is measured in meters.

x = i + 2j + 2k

unit vetor of x = (i + 2j + 2k)/3        ..................1

this is also a unit vector in the direction of force

force = 15N in magnitude so

vector force F = 15(unit vector in the direction of force)

                F = 15(i+2j+2k)/3 = 5(i+2j+2k)         .............2

displacement vector OP =  (7-1)i + (2+3)j + (5-4)k = 6i +5j +k     .............3

workdone = F.dr = F.OP = 5(i+2j+2k).(6i+5j+k)

                                  =5(6+10+2) = 90 joules