(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Question:

"Find the unit tangent, normal and binormal vectors T, N, B, and the curvature of the curve

x = 4t, y = -3t^2, z = -4t^3 at t = 1."

Answer:

T = 0.285714285714286 i - 0.428571428571429 j - 0.857142857142857 k

N = -0.75644794981871 i + 0.448265451744421 - 0.476282042478447 k

B = 0.588348405414552 i + 0.784464540552736 j - 0.196116135138184

ϰ = 0.0445978383113072

2. Relevant equations

N = dT/dt / |dT/dt|

3. The attempt at a solution

I tried to use the equation from the "Relevant equations" part above. I know there are alternative ways but I want to figure out what I am doing wrong for this method.

I (successfully) get the unit tangent vector to be:

T = (4 i - 6t j - 12t^2 k)/sqrt(4^2 + 6^2 * t^2 + 12^2 * t^4)

T = 2/7 i - 3/7 * t j - 6/7 * t^2 k

I (unsuccessfully) get the unit normal vector to be:

N = (3/7 i - 12/7*t k)/sqrt( (3/7)^2 + (12/7)^2 * t^2)

What am I doing wrong?

Any input would be greatly appreciated!

Thanks in advance!

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# Unit tangent, unit normal, unit binormal, curvature

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