Tangential and Normal Components of Acceleration

Question

Find the tangential and normal components of the acceleration vector for the curve →r(t)=⟨4t,3t^2,4t^4⟩ at the point t=2

a(2) = ? T + ? N

Answer 1

Here is how I solved it

First I found all the components of v and a by taking first and second derivatives of the components of r

Next the tangential component of a = v * (a v)/(v v)

Finally the normal component of a is simply a - tangential component of a

The exact answers are cumbersome, but are approximately as follows

a tangential < 6, 18, 192 >

a normal < -6, -12, 0 >