I'm asked to find the osculating plane and the curvature of the curve
$r(t)=(a\cos(t)+b\sin(t),\, a\sin(t)+b\cos(t),\, c\sin(2t)),\, t\in \mathbb{R}.$
To find the osculating plane, first I tried to compute the binormal vector using the formula
$$B(t)=\dfrac{r'(t)\times r''(t)}{||r'(t)\times r''(t)||}\,,$$ but the result got very long. Also, the point on which I am supposed to find the osculating plane is not given.
For the curvature, I have a similar problem, since I'm trying to use the formula
$$\kappa=\dfrac{||r'(t)\times r''(t)||}{||r'(t)||^3}.$$
I have no idea whether I'm on the right track. I appreciate any help!