# How do I find the unit tangential vector and the unit normal vector?

I'm given that a particle travels counter-clockwise on a circle centered at the origin with radius 2. It lies in the $$xy$$-plane and I am also given that $$r(-4) = \langle\sqrt{2},\sqrt{2},0\rangle$$.

I know that the unit normal vector and unit tangential vectors are perpendicular the entire time because it is a circle and has a constant speed.

I also know that the $$z(t)$$ component for the two vectors will be $$0$$. I just don't know how to find the $$x(t)$$ and $$y(t)$$ components

I need to figure out what $$T(-4)$$ and $$N(-4)$$ are (unit tangential vector and unit normal vector).

For a circle, the normal vector is in the direction along the radius. Depending on your convention, you can have normal vector pointing "in" or "out": $$N(-4)=\pm\left(\frac{\sqrt 2}2,\frac{\sqrt 2}2,0\right)$$ The tangential vector, as you mentioned, is in the $$xy$$ plane, and it's perpendicular to $$N$$. You can either use the $$N\times\hat z$$ cross product, or just rotate $$N$$ by $$90^\circ$$. It is important to note that $$T$$ is not only perpendicular to $$N$$, but also it is along the direction of motion. So $$N(4)=\left(-\frac{\sqrt 2}2,\frac{\sqrt 2}2,0\right)$$