Plane in R^3/Linear form/1/Exercise

Let

${}U=\langle {\begin{pmatrix}4\\6\\7\end{pmatrix}},\,{\begin{pmatrix}3\\-3\\8\end{pmatrix}}\rangle \subseteq \mathbb {R} ^{3}\,.$

Find a linear form ${}f\colon \mathbb {R} ^{3}\rightarrow \mathbb {R}$ such that ${}U=\operatorname {kern} f$ holds.

Create a solution