Let $0 < r < b$ and let $X$ be the point on the torus that is given by $$X = i((b + r \cos \theta) \cos \phi) +j((b + r \cos \theta) \sin \phi) + k(r \sin \theta)$$
Show that the vectors $$\frac{\partial X}{\partial \theta} \times \frac{\partial X}{\partial \phi} \quad \text{and} \quad \frac{\partial X}{\partial r}$$ are parallel.
To do this, I found ∂X/∂θ, ∂X/∂ψ and ∂X/∂r by differentiating with respect to the given variables,then found the cross product of ∂X/∂θ × ∂X/∂ψ. But then when I found the dot product of ∂X/∂θ × ∂X/∂ψ and ∂X/∂r it came out to be -r(b + r cos θ) which is not 1.
I'm just wondering if I've used the wrong method at any point or missed something obvious? thanks