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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
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