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Ev(Unit Vector) and projection of a vector in a dot product

  1. Dec 3, 2011 #1
    So my book says

    Lets suppose,

    We have two vector v and u

    w=projection of u ev= unit vector θ=angle between the two

    w=(u.ev)ev or w=( (u.v)/(v.v) )v

    Now, the second equation is fairly easy to understand if we understand the first one because ev= v / |v|

    What is bothering me is I have no idea why w=(u.ev)ev.

    It would be more reasonable, as per me, if w=(u.ev)

    But that is not the case.

    Why is that extra ev lingering around in the equation.

    ANY IDEAS?
     
  2. jcsd
  3. Dec 3, 2011 #2

    mathman

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    Science Advisor
    Gold Member

    w is a vector parallel to ev. (u.ev) is a scalar (± length of w), so you need the entire expression to define the vector w.
     
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