- #1

danago

Gold Member

- 1,122

- 4

**[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]

[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.