Solution
= Solution
The <dot product> is $\mathbf u_+\cdot\mathbf u_-=-\cos\theta\sin\theta+\sin\theta\cos\theta=0$. Each planar vector is perpendicular to $\mathbf u_3$ because its third component vanishes. Each has norm one, so the three vectors form an <orthonormal eigenbasis>. This also follows from the <spectral theorem> for the real symmetric coefficient matrix.