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

  • Thread starter danago
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  • #1
danago
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[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.
 

Answers and Replies

  • #2
Dick
Science Advisor
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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.
 
  • #3
danago
Gold Member
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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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