Find the vectors T, N, and B at the given point.

Question

anonymous · Answer

$$r(t) = \left\{ t^2, (2/3)t^3, t \right\},     Point =    (4, 16/3, 2)$$

anonymous · Answer

I got that 

$$r' = <2t, (4/3)t^2, 0>$$
and
$$|r'| = \sqrt(5t^2 + 16t^4/9)$$

anonymous · Answer

I'm not understanding how to find the vectors at that point.

perl · Answer

there is a TNB frame

perl · Answer

you can do most of this with maple

perl · Answer

For a particular curve C, the TNB-frame is the coordinate system determined by T(t), N(t), and B(t), the unit tangent vector to C at t, the unit normal vector to C at t, and the binormal vector to C at t.  These three vectors are always mutually orthogonal

anonymous · Answer

I just now got that $$T = <2t/2t^2 + 1, 2t^2/2t^2 + 1, 1/2t^2 + 1>$$

but that is showing up as wrong. I just used T = r'/|r'|

anonymous · Answer

Is maple a type of software used to solve these?

perl · Answer

yes

anonymous · Answer

is it online and free?

perl · Answer

your r'(t) is wrong

anonymous · Answer

Yeah it's <2t, 2t^2, 1>

perl · Answer

|dw:1411776421231:dw|