Given the vector: $$ \vec{u}=-7\hat{i}-7\hat{j}+7\hat{k} $$
I need to find another vector $\vec{v} $ that is parallel to the $xy$ plane and perpendicular to the vector $\vec{u} $ .
How can I do it?
I know that any vector that is perpendicular to $\vec{u}$ must satisfy $\vec{u}\cdot \vec{v} =0$ . But how does this help me with finding such a vector?