Find the Tangent and Normal Vectors

[futureengineerpls]

Hi Everyone,

I'm currently studying for my maths exam and I'm stuck on one of the questions. I need to Find the Tangent and Normal vectors and then the curvature. The equation for the curve is:

r(t) = (t, 1/2t², t²)

my working is attached, if anyone can help me out and show me where I went wrong I'd appreciate it.

EDIT
I just realised, should |r'(t)| = 1+sqrt(5)t instead of 1+3t?

 

[futureengineerpls]

Sorry, didn't realise the photo was side ways when I uploaded it.
My bad.

 

[mmm4444bot]

Sorry, didn't realise the photo was side ways when I uploaded it.

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