Differential forms vanishing at $T_p\mathbb S^2$

Question

I want to find differential 1-forms and 2-forms vanishing at $T_p\mathbb S^2$. First of all, I find the the tangent plane $T_p\mathbb S^2$ to the sphere $\mathbb S^2$ given by the equation $$x^2+y^2+z^2=1$$ $\mathbb S^2$ is the level surface $f(x,y,z)=0$, where $f(x,y,z)=x^2+y^2+z^2-1$. Hence, at any point $p=(x,y,z)\in\mathbb S^2$ the normalized gradient $\nabla f(x,y,z)=(x,y,z)$ is orthogonal to the surface. Therefore, the tangent space is the space in $\mathbb R^3$ orthogonal to the span of $\{p\}$. For example, let $p=(x_0,y_0,z_0)$, then the tangent plane of the sphere at $p$ is given by $$x_0x+y_0y+z_0z=1$$ Now, my question is, how is this related to the differential 1-forms and 2-forms on $\mathbb R^3$?