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Help with dot products - How can the dot product be a vector quantity?

  1. Oct 31, 2007 #1

    danago

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    Gold Member

    [tex]\overrightarrow r (t)[/tex] is a vector valued function given by:

    [tex]
    \overrightarrow r (t) = x(t)\overrightarrow i + y(t)\overrightarrow j
    [/tex]

    if [tex]h(t) = \left| {\overrightarrow r (t)} \right|[/tex], show that the following is true:

    [tex]
    \overrightarrow r (t) \bullet \overrightarrow r '(t) = x(t)\overrightarrow i + y(t)\overrightarrow j
    [/tex]


    Now, my first question is: how can a dot product of two vectors possibly be another vector? Isnt the dot product always a scalar quanitity? Am i correct in saying this, and is there a typo in the question, or am i completely missing something?

    Thanks in advance,
    Dan.
     
  2. jcsd
  3. Oct 31, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    If that's the question, it makes no sense. It is true that (r(t).r(t))'=2*r(t).r'(t), which is the only thing that that even sort of resembles.
     
  4. Oct 31, 2007 #3

    danago

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    Gold Member

    Alright thats good to hear. I was going through some past exam questions which had been re-written and published into a book, and this one came up, and yea, it didnt look right to me. Well thanks very much for confirming that :smile:
     
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