Directional derivative

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?


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


The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving