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Math Help - vector and dot product

  1. #1
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    vector and dot product

    1. Work done is the product of the force and the distance travelled in the direction of the force. Calculate the work done when the force F=5i+3j moves an object from point P = ( -2 , 3 ) to point Q = ( 1 , 6 ).

    2. Given thati = (1, 0) and j = (0,1), u= 2i +j, w= 3i+4j and v = i-3j
    find,
    a) u . v + u .w
    b) (u.v)(u.w)
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  2. #2
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    Quote Originally Posted by dorwei92 View Post
    1. Work done is the product of the force and the distance travelled in the direction of the force. Calculate the work done when the force F=5i+3j moves an object from point P = ( -2 , 3 ) to point Q = ( 1 , 6 ).

    2. Given thati = (1, 0) and j = (0,1), u= 2i +j, w= 3i+4j and v = i-3j
    find,
    a) u . v + u .w
    b) (u.v)(u.w)
    1. W=F.s=(5i+3j).(3i+3j)=15+9=24

    2. u.v=2-3=-1
    u.w=6+4=10

    a) u.v+u.w=-1+10=9

    b) (u.v)(u.w)=-1.10=-10
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  3. #3
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    could u write the working for qn 1?
    i dont understand how u derived at 24...
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  4. #4
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    Quote Originally Posted by dorwei92 View Post
    could u write the working for qn 1?
    i dont understand how u derived at 24...
    F = 5i + 3j

    \Delta r =  (1,6) - (-2,3) = 3i + 3j

    F \bullet \Delta r = (5 \cdot 3) + (3 \cdot 3) = 15 + 9 = 24
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  5. #5
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    why is it equivalent?
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  6. #6
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    Quote Originally Posted by dorwei92 View Post
    why is it equivalent?
    the basic definition of displacement ...

    change in position = final position - initial position
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