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What is the principal unit normal vector for the curve:

$${\bf r}(t)=(3t+1){\bf i} +e^t {\bf j}$$

...at the point $P=(1,1)$?

$\cfrac{\sqrt{10}}{10} {\bf i} -\cfrac{3\sqrt{10}}{10}{\bf j}$

$\cfrac{3{\bf i}-{\bf j}}{\sqrt{10}}$

There is no unit normal vector for this curve at this point.

$-\cfrac{\sqrt{10}}{10} {\bf i} + \cfrac{3\sqrt{10}}{10}{\bf j}$

$\cfrac{3{\bf i}+{\bf j}}{\sqrt{10}}$