How can I find the tangential and normal components of the acceleration vector at $t=2$ for: $r(t)= t\mathbf{i} + \displaystyle\frac{t^2-1}{2}\mathbf{j} + \displaystyle\frac{t^2+1}{2}\mathbf{k}$
I found the velocity vector at $t=2$ to be $\langle1,2,2\rangle$ and acceleration vector to be $\langle1,0,1\rangle$
What goes next for the tangential and normal components of acceleration vector?
The tangential component of $\vec a$ is given by $$ a_{tan} = \frac{\vec a \cdot \vec v}{\|\vec v\|} $$ The normal component is given by $$ a_{norm} = \left\|\vec a - \frac{a_{tan}}{\|\vec v\|}\vec v \right\| $$