Directional derivative

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Suppose I have a path [tex]\vec{r}(x,y)[/tex] and some vector [tex]\vec{a}(x,y)[/tex].
Question is: how do I find the tangential and perpendicular component of a along the path r at a given point?

For tangential component, I'd just take the projection of a on r with dot product (I guess this's correct). But what about perpendicular one?
 

Hootenanny

Staff Emeritus
Science Advisor
Gold Member
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HINT: The dot product of two perpendicular vector lines is zero.

~H
 

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