(Solved): Find vectors \( \vec{w}_{1} \) and \( \vec{w}_{2} \) such that \( \vec{w}_{1} \) is parallel to \( ...

Find vectors \( \vec{w}_{1} \) and \( \vec{w}_{2} \) such that \( \vec{w}_{1} \) is parallel to \( \vec{u}=3 \overrightarrow{\mathbf{l}}-\overrightarrow{\mathbf{J}}, \vec{w}_{2} \) is orthogonal to \( \vec{u} \) and \( \vec{w}_{1}+\vec{w}_{2}=6 \overrightarrow{\mathbf{l}} \).