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Parallel/Orthogonal in Calc 3.

  1. Sep 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Let vector 'v'=<1,-1,5> and vector 'w'=<40,-19,-1>. Represent 'w' in the form of 'w'='g'+'h',
    where 'g' is parallel to 'v', and 'h' is orthogonal to 'v'. This is related to the dot product. But I don't know where to begin

    2. Relevant equations
    'v' is a vector. 'g' is a vector. 'w' is a vector. 'h' is a vector

    3. The attempt at a solution
    So far I set up an equation <40,-19,-1>='g'+'h'
    I doubt this is right so far. I know that g has to be a multiple of v and h has to = 0 in order for it to be orthogonal.
  2. jcsd
  3. Sep 8, 2011 #2


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    Homework Helper

    well what do you know about dot products? in particular consider
    [tex]w \bullet v [/tex]
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