SOLUTION: Evening Everybody Stuck on this question. (trying to get back in to the swing of things so i can enrol on a course) i) Given that F.r is the work done by a force F in movi

Algebra ->  Length-and-distance -> SOLUTION: Evening Everybody Stuck on this question. (trying to get back in to the swing of things so i can enrol on a course) i) Given that F.r is the work done by a force F in movi      Log On


   

Question 366114: Evening Everybody
Stuck on this question. (trying to get back in to the swing of things so i can enrol on a course)
i) Given that F.r is the work done by a force F in moving a body through displacement r. Find the work done by the force F= 3i+7k. if it causes a body to move from the point A with coordinates (1,1,2) to the point B with coordinates (7,3,5)
ii) Obtain unit vectors in each of the directions of f=i+j+3k and s=2i-j+k. Hence show that 48/sqrt66 joules is the work done when a force of magnitude 6 newtons in the direction f moves its point of application a distance 2 metres parallel to s .
Really appreciate help on this.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find r=(7,3,5)-(1,1,2)=(6,2,3)
F%2Ar=(3,0,7)*(6,2,3)=3%286%29%2B0%282%29%2B7%283%29=18%2B0%2B21=highlight%2839%29
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f=(1,1,3)
abs%28f%29=sqrt%281%5E2%2B1%5E2%2B3%5E2%29=sqrt%2811%29
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U%5Bf%5D=(1%2Fsqrt%2811%29,1%2Fsqrt%2811%29,3%2Fsqrt%2811%29)
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U%5Bf%5D=(sqrt%2811%29%2F11,sqrt%2811%29%2F11,%283%2Asqrt%2811%29%29%2F11)
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s=(2,-1,1)
abs%28s%29=sqrt%282%5E2%2B%28-1%29%5E2%2B1%5E2%29=sqrt%286%29
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U%5Bs%5D=(2%2Fsqrt%286%29,-1%2Fsqrt%286%29,1%2Fsqrt%286%29)
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U%5Bs%5D=(sqrt%286%29%2F3,-sqrt%286%29%2F6,sqrt%286%29%2F6)
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W=6U%5Bf%5D%2A2U%5Bs%5D=12%28U%5Bf%5D%2AU%5Bs%5D%29



W=6U%5Bs%5D%2A2U%5Bs%5D=%2848sqrt%2866%29%29%2F66%29%29
which is equivalent to 48%2Fsqrt%2866%29