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

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$$\overrightarrow r (t)$$ 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?

Dan.

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