- #1
jegues
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Homework Statement
See first figure.
Homework Equations
The Attempt at a Solution
See second figure.
When I set [tex]t = 0[/tex] in [tex]\vec{r(t)}[/tex] I get [tex]0\hat{i} +2\hat{j} + 1\hat{k}[/tex].
I know this is a vector and not a point but it has the same "coordinates" as the point they are asking us to find the unit tanget at. Is there a reason for this?
So I took the derivative of [tex]\vec{r(t)}[/tex] to get [tex]\vec{v(t)}[/tex]. I tried to get the magnitude of [tex]|\vec{v(t)}|[/tex], but I end up with a pretty messy expression.
At this point I wasn't to sure how to proceed so I tried to make sense of things the best I could.
When I evaluate [tex]\vec{r(0)}[/tex] it brings me to the point (the tip of the vector [tex]\vec{r(0)}[/tex]) at which I want to find the unit tangent vector.
So if I evaluate [tex]\frac{\vec{v(0)}}{\vec{|v(0)}|}[/tex] I should be able to get the unit tangent vector at the desired point.
I have a feeling this is wrong because [tex]\vec{r(0)}[/tex] is still a vector and this is not the same as a point.
Does anyone have any suggestions for me? Or can correct my thought process?
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