How to Find Tangential and Perpendicular Components of a Vector Along a Path?

[gulsen]

Suppose I have a path $$\vec{r}(x,y)$$ and some vector $$\vec{a}(x,y)$$.
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]

HINT: The dot product of two perpendicular vector lines is zero.

~H