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

[danago]

$$\overrightarrow r (t)$$ is a vector valued function given by:

$$\overrightarrow r (t) = x(t)\overrightarrow i + y(t)\overrightarrow j$$

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

$$\overrightarrow r (t) \bullet \overrightarrow r '(t) = x(t)\overrightarrow i + y(t)\overrightarrow j$$

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.

 

[Dick]

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.

 

[danago]

Alright that's 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