Calc3 - Find Tangent, Normal, and Binormal Vectors along with Curvature of the Curve.

[jetter2]

r(t) = <3sin(t), 3cos(t), 4t>

Find the Tangent, Normal, and Binormal Vectors to this Curve. Then find the Curvature.

I used the following Formula's. (I will use bold cap letters to signify a vector)

T= r'/|r'|
N= t'/|t|
B= TxN
K= |r' x r''| / |r'


Finding Tangent vector I take r' = <3cos(t), -3sin(t), 4>
|r'| = (3²+4²) = 5 (cos - sin = 1, so its just (9+16)^1/2

T=<3/5 cos(t), -3/5 sin(t), 4/5>

Finding Normal Vector:
t' = <-3/5 sin(t), -3/5 cos(t), 0)
|t'| = [(3/5)²]^1/2 =3/5
N= <-sin(t), -cos(t)>


Finding Binormal Vector
B=TxN

I crossed the two vectors and got (4/5 cos(t), -4/5 sin(t), -3/5>

K= (153^1/2)/125

Below is a pic of my work..does it look right?

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