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    I don't understand the part about "projecting" CD?
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    (Original post by GPODT)


    I don't understand the part about "projecting" CD?
    It's basically what they show you in the diagram - essentially it's the "component" of CD along the bottom line (in the same way that you can split a vector into horizontal and vertical components).

    (Do you do Mechanics? It's the same principle as resolving forces)
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    (Original post by davros)
    It's basically what they show you in the diagram - essentially it's the "component" of CD along the bottom line (in the same way that you can split a vector into horizontal and vertical components).

    (Do you do Mechanics? It's the same principle as resolving forces)
    I'm doing M3 atm but I'm still baffled. if they resolved it along the bottom line surely it would be (3)costheta ,where theta is the angle at C?
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    (Original post by GPODT)
    I'm doing M3 atm but I'm still baffled. if they resolved it along the bottom line surely it would be (3)costheta ,where theta is the angle at C?
    Edit: I originally posted a response saying there must be a difference related to the fact that it's 3D not 2D, and my 3D visualization skills are pretty poor, but looking at the diagram again, surely the point is that the projection is 3cos theta - if you look at the diagram the length marked is 3/root(50), so cos theta = (3/root(50)) / 3 (because length CD = 3) = 1/root(50). Working in reverse: projection length = 3cos theta = 3/root(50).
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    (Original post by davros)
    Edit: I originally posted a response saying there must be a difference related to the fact that it's 3D not 2D, and my 3D visualization skills are pretty poor, but looking at the diagram again, surely the point is that the projection is 3cos theta - if you look at the diagram the length marked is 3/root(50), so cos theta = (3/root(50)) / 3 (because length CD = 3) = 1/root(50). Working in reverse: projection length = 3cos theta = 3/root(50).
    Sorry for the confusion but my question is what did they do in this step? Could you explain what they done here:

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    (Original post by GPODT)
    Sorry for the confusion but my question is what did they do in this step? Could you explain what they done here:

    That looks like the standard formula for the dot product: a.b = |a||b|cos(theta), rearranged to give the length in question.
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    (Original post by davros)
    That looks like the standard formula for the dot product: a.b = |a||b|cos(theta), rearranged to give the length in question.
    But the dot product has |a| multiplied by |b|.. the image I uploaded only has the modulus of one vector
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    (Original post by GPODT)
    But the dot product has |a| multiplied by |b|.. the image I uploaded only has the modulus of one vector
    Sorry - I saw your quote earlier and then forgot to reply!

    We want the projected length of vector a, which we agreed was given by (length of a) times cosine of angle i.e. |a|cos\theta

    Now, a.b = |a||b|cos\theta

    Therefore
    |a| cos\theta = a.b / |b|

    which is what your uploaded image shows.
 
 
 
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